There are random issues like this (e.g., not being able to type in the text input) that just seem to randomly happen. I've talked to some other knowledgeable people who have confirmed my hunch:
Our chat app is a "legacy app" -- it was coded many years ago for Flash Player 6 (I simply added on many features such as the voice and video, but it's still a Flash Player 6 app). All newer version of the Flash Player are *supposed* to be backwards compatible with all legacy Flash apps, but actually it's not perfect backwards compatibility, and Adobe probably isn't very concerned about rare cases such as ours.
So the real solution is for us to design our own chat app from the ground up, for Flash Player 11+. (We need funding for that.)
In the meantime, what usually works when people have these random issues is to try another browser (Chrome, IE, or Firefox).