Here is another suggestion, maybe you want to check if your winsock is slightly screwed up?
http://www.cexx.org/lspfix.htm
Note: spybot (v1.3) by default doesn't remove new.net (which affects the winsock) , because it is in the ignore list. you can acces the ignore list from the advanced menu. here is a thread that explains what is in the ignore list
http://www.wilderssecurity.com/showthread.php?t=33199
I'm not sure what else to check, considering that it seems like your initial connection is fine, but after a while, you "lose" internet access to new site (browsing) but, stuff that is connected when it was working aren't disconnected (im, p2p, etc).