Try it for yourself. Take a copy of a JPEG and open it and save it. Then open it again and look at a 100% crop. You won't see any difference. Do it 4 or 5 more times and you'll start to see a real problem. I shoot RAW because I like the flexibility and I can recover from my mistakes and still have a publishable image. If I blow a highlight in a JPEG there is no getting it back...in RAW you can.

You definitely should save your edited files in TIF or a lossless format so that you do not get into 3rd or 4th or 5th generation JPGs.