This chat is hosted at envolve.com so there must be some limit for total number of people in all chatrooms on all hosting sites. So if there are many people elsewhere (where this chat addon is used) you'll see 'The chat is full' message.
Doesn't explain why it shows it's full everytime you reconnect and reenter the forum even though you were in the chat right before reconnecting. It would be cool if those folks out there recognized their bugs and started actually doing something about it.