Odd Problem

If it only affects audio and not video, it's unlikely the TV itself (both audio and video are digital, so a reception issue would affect both). It's a very unusual issue, but I would suspect the issue is in the surround sound system. Perhaps when the 2nd TV is turned on, a ground loop is created, causing the surround system to go quiet.

I would first try recreating the issue, then unplugging the antenna lead from the 2nd TV. If that restores audio through the first system, it's almost certainly a grounding issue.