Continuing the saga:
I forgot to describe the exact symptom I have been experiencing. Here goes. After the AC failed suddenly on my '04 Corolla, I was advised to replace the compressor. When I picked it up with the new compressor in place, the AC seemed to be going blazes, but in the next couple of days it became weaker and weaker. I took it back and they recharged it. Again, seemed to be cooling very effectively at first, but it degraded over the next couple of days. When I went back, they recommended replacing the compressor, by process of elimination, and they said they were certain there were no leaks.
I decided to wait until the weather warmed up somewhat so that I'd feel more confidence in my evaluation of new results.
Today the weather started to warm up. I printed out the answers and comments from my other question and took the car back to the shop. Based on advice given at the other thread, I asked what was wrong with the compressor that failed. The manager just shrugged and said it was no good. I asked how they were able to determine that there were no leaks, and he said that when they connect it to the machine for recharging, step one is to suck out the refrigerant that's in the system, converting the gas to a liquid in the process. The manager said that the amount withdrawn was exactly the same amount they had put in the previous week, and that's how he knows there are no leaks.
Is that logic valid? Today they agreed to check the dryer and the expansion valve but in the meantime I would like to understand the situation better.