Q: My A/C belt is leaking and I want to know if I have to recharge it.

My AC has been on and off recently. It will never come out cold right away, the air will be lukewarm for about 15 min. and then finally becomes cold. Or, if i first start on the car after it has been a while, the AC won't work, but if i turn off the engine and come to my car like 10 minutes later, AC will then work. I took it to the shop, where I got a "full service" of vacuum and refill coolant. The next day, I still had the same issue, but the cold air came on faster and it was a LOT colder. they said there was no leak. Its been about 1.5 weeks and today is a super hot day-- turned on the AC, and it was HOT air when I had setting on full a/c blast while driving for 20 minutes. Shop said now they see a leak, and they can replace AC belt AND do a "re" something, I wasn't able to hear the word (i am assuming re-vacuum or refill coolant) for $200. I want to know if this avg. price... and since I already paid for the "re__" thing before, am I going to be paying for the same thing again?

My car has 169900 miles.
My car has an automatic transmission.