I see your case has been replied to by the Customer Support representative, a few days prior. Would you be able to check for that support email response from 9/12, and let us know if the suggestions there had any effect by replying back to that email thread?
The problem is spreading, my colleague is now also affected by untimely disconnections. Personally, it's worse and worse. I also noticed, when connecting to remote computers with a solution other than yours, that their LogmeIn client disconnects also. An exclamation point appears and indicates "inaccessible, offline", before returning online.
It is no longer possible to work with your software, I am constantly disconnected and I have to close my browser to reconnect to logmein, otherwise it runs in a vacuum. It's getting long.