Google's Adsense program was a great program while I was able to use it. About 2 years ago I was making about $25 a month from adsense on one of my sites so what do they do? They banned me. I received an email that said I had been falsifying impressions. I went to the site and asked what I was doing incorrectly and if I could be allowed to rejoin the program and they said no. That is all I was given. So now 2 years later I finally figured out what I was doing incorrectly and why my site was banned.
I went to their online appeal forum and sent a request. This was over 1 month ago and they still have not sent a reply. 2 years ago I was banned why don't they think I learned my lesson from being banned for that long?
You can probably learn by reading through their TOS... whatever it is that you were doing that resulted in them banning you... it's probably listed there somewhere. You can try emailing them again, but I suspect it's completely up to them whether they want to let you back into their program or not.