Yeah I've been gettin that 4001 error code a lot too. But it does more then just boot me out the server. It also closes the SWTOR game on me as well. So I have to re-boot the game and re-enter my server. I'm posting this on 2/15/2014 and I'd say just today alone it's done this about 4 or 5 times. Would be cool to find out what the issue is. I was about to start tinkering with my security settings and firewalls, even run a tracert... until I read this forum and saw all the other people having this issue.
Bioware, please help to fix this, even if it's on our end.
Edit: Oh and I haven't had this problem before, it just started doing this to me today (note: I have not updated my firewall or security or microsoft files between now and the last time I played). So I know it isn't my firewall. Of course I know computers well enough to know that it also could be the firewall and now all of a sudden it's deciding to block SWTOR. But usually it doesn't just happen on it's own. So iunno. Any help will be much appreciated.