The mail provider wouldn't cause your whole connection to fail, could you be more specific as to what is going wrong? Only two problems I can see is either your ISP drops your connection (unlikely, unless you have wireless or crap-tier ISP) or you have internal overheating problems (very unlikely).
Try seeing if there's a problem with you NIC card:
type ping 127.0.0.1
If you get a response, its your connection. If you don't, its your computer.
Running through proxy servers might also cause uploads/downloads to fail at random places. I really
don't think you're using a proxy