More info....
Ok, so I have toasted a total of 3 characters now.
The problem occurs when I try to zone. In the middle of the zoning process, the game just hangs. The 3 times it has happened to me, I hit CTRL-ALT-DEL and killed the process. I don't know if I should have waited for the game to boot me back to the login screen, but I kind of got tired of waiting.
It doesn't happen all the time, but when it does, it appears to corrupt my character, or something of that nature, because if I create a new character, everything works just fine again.
Creating new characters every couple days has gotten kind of tedious though.
Any ideas?