If I connect this machine via a hub (it says it's a hub, but it could well be switching) it works fine, and I can renew IPs.
The vr(4) driver in FreeBSD 6.3 (used for the NICs on ALIX boards) seems to have problems detecting link-up events sometimes (as it has to when you reboot that machine and it's directly connected to the ALIX, as the link will inevitably flap while it's rebooting). Unfortunately there's no solution yet; the problem only seems to be fixed in FreeBSD 7.0, and the changes are too extensive for a simple backport to 6.3.
See also
http://m0n0.ch/wall/list/showmsg.php?id=344/90