I ended up having to create a second account on my private IMAP server (don't get me started why ...), and it turns out Thunderbird (at least v3beta) did not like this. It's limited to only one account per server. I tried using a different CNAME for the server, and albeit Thunderbird now lets me configure the second account, it only works until you restart TB. The final solution (thanks Dmose) is to create a new A-record with the same IP, then TBird happily works with the second accounts as well.