I’m posting this here because it took me more than 20 minutes of googling to find the answer (and I’m an Adobe employee).
The Adobe Connect uses Flash and sometimes if you do an update to Flash on your system, Connect gets into a bad state. The way you’ll see this is that when the Add-in tries to launch it will get stuck with a small window that says “Loading Adobe Connect…” that never finishes.
The way to fix this problem is to uninstall Adobe Connect. Unfortunately, Adobe doesn’t make it easy for you to do that. there is no uninstaller and no information on the Adobe web site. Here is where the add-in is installed
Delete that directory and you have now uninstalled the add-in. Your connect sessions will now be hosted in your web browser until the next time you need add-in functionality, at which time you’ll be prompted to re-install it.
Hopefully this solves your problem and you found it faster than I did.