Luckily, as elements, none of the six materials "break down" in a system. The trick comes in making sure enough of it cycles through the system, in accessible form, without being lost or bound up irretrievably.
In this post, I'll talk chiefly about nitrogen, one of the largest issues for maintaining healthy gardens. Available nitrogen particularly concerns those of us trying to grow food crops, since capturing and transforming huge numbers of electromagnetic joules into food calories requires heavy feeding on the part of the plant.
Chemistry section, to ensure we're all on the same page - skip the blue text if you don't need it:
Nitrogen is a relatively inert, colorless, odorless gas in its default form. It's 78% of the atmosphere. It's also a critical component for every protein in existence, and remember that proteins aren't just muscle tissue and meat, they comprise the fundamental chemical architecture for all biochemical processes. No protein, no life. So, nitrogen's really important.
It's also bizarrely rare in the soil, given its incredible abundance in the atmosphere. However, gaseous nitrogen is in the form N≡N, that is, two nitrogen atoms triple-bonded to each other. This triple bond is extraordinarily stable, which is why gaseous nitrogen is really nonreactive. Therefore, it's also really energy expensive to crack open, in order to get access to the nitrogen for purposes like protein-making.
So energy expensive and complicated, in fact, that only a relatively small number of organisms can do it, using fancy things like iron-molybdenum complexes. There are a number of these microorganisms in the soil, some free, others symbiotically bound up to plant roots. They replenish available soil nitrogen, and in doing so help ensure the continued existence of all other life on earth.
The other source of available soil nitrogen is non-atmospheric. Things with available nitrogen, like animal poop and dead chipmunks and rotting plants, decay in the soil, and their nitrogen contents become available for other critters. If you are having dim memories of science class and "The Nitrogen Cycle" at this point, check out this awesome public domain graphic from the EPA:
This basic nitrogen cycle explains the introduction of sheep-pasturing to European farming - farmers figured out that land needed to be left fallow for several years after repeated plantings, or else pretty soon nothing worthwhile would grow on it (several years allowed soil bacteria and nitrogen-fixing plant symbiotes to replenish the nitrate supply.) On the other hand, just one season of letting sheep graze and poop in a field made it ready to go the following year - the sheep's guts liberate the nitrogen in the things they eat, and a lot of it ends up going out the other end. The sheep manure rejuvenates the field, making it suitable for heavy-feeding crops once more.
In the last century, we learned a number of excellent tricks to short-circuit this system. First, you can find a preexisting source of huge amounts of animal droppings, like coral atols in the geographical middle of nowhere, using the military to protect you if necessary, and then spend vast quantities of energy mining and shipping that stuff to your farm, where you dump it on your fields, Most of the urea and uric acid in it, the sources of nitrogen, get dissolved and washed away without doing much, but this kind of shotgun approach will certainly add nitrogen. Or, you can spend that energy in a slightly less insane fashion, and pull atmospheric nitrogen into usable forms (the Haber process), the doing of which currently consumes 1-2% of the entire world's yearly energy output. As an interesting historical tangent, Germany lacks access to any significant natural nitrogen sources (like guano deposits, or nitrate mines) for explosives, and without the Haber process, it would likely not have been able to wage World War I (the allies mind potassium nitrate, i.e. saltpeter, from Chile.)
So, although it's a neat set of tricks, they all depend on cheap readily available energy, which means they depend on fossil fuels. How can we build sustainable, non-petrochemical based, but still nitrogen-rich soil?
We just follow the standard permaculture protocol, "mimic nature with intention and forethought."
First, we ensure the presence of nitrogen-fixing plants, the ones whose roots house the symbiotic bacteria turning atmospheric nitrogen into plant-usable nitrates. This means legumes most of the time - beans, peas, alfalfa, soybeans, etc. Other nitrogen-fixers with multiple uses include clover, lupines, and rooibos. Nitrogen fixing plants which themselves provide food, fodder, beauty, and so forth, exemplify "stacked functions", a fundamental permaculture principle I discuss in another post, which boils down to "everything should exist in relationships such that, by being what it is, it performs multiple duties". If you have the luck to be in one place for the long term, a few awesome trees and shrubs are nitrogen fixers, among them black locust , the Persian silk tree (which we Southerners call a mimosa), and the Siberian seaberry.
Personally, I like to use clover for cover-cropping. Lawns should be a mix of grass and clover, which provides natural fertilizer and bee forage, and which was the case until Monsanto (having invented Roundup, which kills all broadleaf plants) poured millions into advertising to convince folks that a "real" lawn was nothing but a nutrient desert of narrowleaf grass. Many different kinds of clover can be used; they provide a pretty, nitrogen-enriching, bee-attracting crop, which can be intercropped with other plants.
Also, crop rotation - you do rotate crops, right? That's like the most basic and easy way to maintain soil health - crop rotations including legumes, and/or occasional "fallow" years of clover or alfalfa or whatnot, will replenish soil nicely, if you can afford to set aside space. Again, it need not be wasted; good choice of cover crops will mean your "unused" field provides plenty of beauty, bee attraction, and green manure. As I'm not big on plowing, I would stick to growing annual cover crops, and chopping them back before they seed, rather than just letting them run rampant then breaking up the soil network by plowing the whole works.
You can also include animals in your rotation, but I have no personal experience with that, so I will remain silent. I plan to rectify this lack of experience later, though. God knows I need more pygmy goats in my life.
Finally, you can replenish soil nitrogen using "waste" material. Remembering always that "waste" is a verb, not a noun - no material is inherently useless and extraneous, we just fail to use it - taking organic matter produced by your household, breaking it down, and returning it to the soil, is a basic method of maintaining soil fertility that humans have used for four thousand or more years.
First, of course, you compost. Kitchen scraps become dirt. I won't dilate on composting, as plenty of good web and book resources already exist to which I can't add much. I will put in a plug for trench composting, for its simplicity, utility, and easy combination with hugelkultur.
Second, take advantage of the constant stream (tee hee) of nitrogen-rich fertilizer you make. Yes, I am totally advocating peeing into jars, then dumping those jars onto your compost pile, or into plastic bags of leaf litter (to make easy homemade leaf mold over the winter, fall waste becoming spring mulch), or for direct application to plant beds once you've diluted it about 10:1. There is much more to be said on the subject, but I'll limit myself to quick bullet points. It's sterile, it doesn't smell once applied, it's gobsmackingly obvious and efficient, and after doing it for a few days, you really realize how, despite a third of the planet lacking reliable clean water access, we in the first world consider it normal to take energy-intensively purified water and piss in it, to the tune of 5+ gallons per day per person. This is why we cannot have nice things, humanity. It's an excellent function-stacking exercise - a waste, which you pay to dispose of, now becomes a free and abundant and infinitely sustainable source of useful fertilizer.
I find that an upcycled 1-gallon glass jar, the kind that apple juice often comes in, provides an easy to use urinal. I also admit to certain mechanical advantages of being male, in this respect. A bucket full of wood shavings or sawdust works even better, as it slows the breakdown of the urea in the urine into ammonia (urea itself is odorless; the metabolites from food and the breakdown of urea to ammonia in water give it the characteristic pee smell), as well as - stacked function! - providing a chance for the wood to "charge" with water and nitrogen, ensuring its speedy breakdown. If like me you have pets, or a spouse with sharp senses, a sealed glass jar prevents odor escape, and the glass won't absorb any smell. If you use wood chips, look for untreated wood, and make sure to thoroughly soak any kiln-dried (lumber) sawdust, before mixing it with soil, as otherwise it lacks the water for fungal and bacterial breakdown. Better still is peeing into a bucket of biochar, to "charge" it with ions and water, but biochar deserves its own post at a later date.
I'm also skipping over humanure, composted human waste, not because it isn't awesome (it totally is) but because I lack enough experience with it directly to add to the extant conversations on it. In the future, though, expect me to pontificate at length on the virtues of poop composting. In the mean time, make use of Milorganite, an idea so breathtakingly amazing that it's unsurprising that only one metropolitan area in the USA does it.