In this thread:
http://www.heroscapers.com/community...ead.php?t=4171
the consensus seemed to be that the official rules set no limits on when or how many times the controller may open the Door. The people who thought so had much higher post counts than me, so I won't argue with them.
Nothing says you can't make a scenario rule against it though. Doesn't even have to be a house rule.