Hi Lance,
I have no experience with Adobe Connect. I believe that maybe the SSL Scanner or filtering at all can cause problems here. Most of the "Web Conferencing" software does not like when we try to modify the traffic, and break. If you look into the access.log, you will probably see some Adobe Connect related lines and their error code. If you have a chance, try to add them to the "ICAP Bypass list", and see whether the traffic goes through then.
I don´t have a better advice at the moment.
Best,
ANdre