I think we've solved the mystery!
Cycling refers to the process of creating your biological filter. Unfortunately, Stress Zyme, despite it's claim, does absolutely nothin' towards this process. There are a couple ways to approach the problem.
1. Cycle with fish. This is what you're in the midst of, most likely. The fish in your tank produce ammonia. The presence of ammonia fosters the growth of bacteria which use the ammonia as a food source (more or less). Ammonia is toxic to fish though, so you have to balance leaving some for the bacteria, but not leaving so much as you harm your fishies. These ammonia-eating bacteria then spit out nitrites. Nitrites also harm your fish...so again, you have to keep changing the water, but leaving a little in there so the next group of bacteria can grow. This group is much slower to colonize, it can take a couple of weeks. When they're settling in your tank, you'll start seeing nitrates in your tank, (they eat nitrites, and spit out nitrates). When you have zero ammonia, zero nitrites, and some nitrates...you have achieved a cycled tank. At this point you only need to change the water when your nitrates get high. Your bacterial colonies are still relatively suscpetible though...so when you do a gravel vac, you're likely to start seeing some small levels of ammonia and/or nitrites.
2.Fishless cycle. Basically the same process as above...except don't use any fish as an ammonia source, you use household ammonia. Kinda tricky, but guarantees your fish won't be stressed in the cycling process.
3. Bio-Spira. This product does what stress-zyme claims to do...sorta. Basically its a mixture of those 2 bacteria, kept refridgerated, and in some kinda of nutrient solution. Purportedly, you can add bio-spira, and a full tank of fish all at once, and achieve an "instant" cycle. I see that as a kind of best case scenario. I've never used the product, but my guess is that more often, its kinda like a big jump start on the cycle.
The good news? If you have nitrates, and nitrites, and no ammonia...you're in the home stretch of cycling your tank. Hopefully your fish have all gotten through the process ailment-free. It is important to keep up with water changes when your nitrite levels are high...not necessarily gravel vacs (since the bacteria colonize in there, and you don't want to keep sucking them out!), but changing out 10-15 percent of the water with fresh water when you have nitrites in the tank.
I'd do a 10-15% water change (not a gravel vac!) every other day (or even every day) or so until you can get a new test kit, or until your water smells like wet dirt.