This issue apparently appeared in Flash Player 11.4 and was fixed in 11.5:
http://helpx.adobe.com/adobe-connect/kb/connect-recording-playback-iss ues-flash.html
But has resurfaced. The meeting recordings were made with Adobe Connect Server 8.2, and include screen sharing that needs to be recorded.
I've downgraded Flash Player to 11.5 on one machine, 11.3 on another and am attempting to make offline recordings of the meeting on both, which I can hopefully distribute to users.
I'm wondering if anyone else has encountered this problem, and what other workarounds they may have used.