We are getting to where the WebChat interface is too unreliable to use.
What happens is similar to what you are describing.
What happens is:
a.) Person A - logs on.. make themselves available.
b.) Person B - logs on.. makes themselves available as well.
c.) Person C - does the same....
at some point person a or b or c.. can have a chat with the others. no problem.
BUT, person A, somehow no longer shows themselves to be available.. from Person B or Person C perspective.
"A" - thinks they are available, because they still show green AVAILABLE...
so now person B and C can't chat with person A... and Person A doesn't understand why no one is communicating.
This happens everyday....
I have looked in logs, but don't see anything too revealing.