There are antiviruses that purge the cgminer.exe file, make sure that you exclude cgminer from your antivirus scans, or restore it after your antivirus quarantined/purged it.
It doesn't remove it. It simply stops it from connecting; it starts, and seems to hang. I disable the AVG anti-virus, and it starts and does everything normally. If I enable the anti-virus while cvg is running, and it continues for a bit then stops. I've added the whole directory as something to exclude from scans but that doesn't do it.
Can you post any error messages that appears when cgminer crashes? Have you checked AVG's network connection permissions? It might be the case that AVG has blocked any network connections for the cgminer program, just like what Norton does. Unblock cgminer if that's the case.