I haven't used the captive portal in ages, but is there a logout button/page that maybe that machine's browser is prefetching?
Itb is already push-out by a jaca script when login succeded (if set to do so).
But a button needs to be pressed to actually logout.
This would show up in the captive portal log.
Right now, I guess "LOGOUT's aren't seen in the portal log.
So 'something' is resetting the portal firewall (the tables ipfw that contain the allowed client IP's).