I know that the only way to dump CYA is to dump water. But it seemed that when my wife was taking care of the pool, it seemed like there was a cycle of using stabilized Cl, until there was an algae bloom, then it would go out of control until you "shocked" your pool with twice the dose for a few days, at which point things seemed to go back to normal again. So, I don't know that for sure, does the algae break down the stabilizer or doesn't it...? I will ask that question at TFP since this place is geared more towards beating things together.
I have since started the BBB method of pool care, and I have never had any problems. I have my TA at around 90, which makes my Ph stable at 7.3. I also just use the liquid shock from the pool store. It is 12.5 strength, and I don't leave it in direct sunlight, it is in the garage. The breakdown is exponential from the way I understand it. It loses its strength faster the higher that it is and slower the lower the percentage. CYA is necessary, not that you said that it wasn't, but it gives the Chlorine something to bond to so that the sun does not burn it off too fast.
My pool is only 8600 gallons, and I am SERIOUSLY considering a SWG, that would essentially free me up to go away on the weekend on occasion without needing to bother anyone.
Basically, check out TroubleFreePool.com, educate yourself, get a good test kit, and spend 5 minutes a day on water chemistry. Everyone will be amazed.