I've been having this problem for a while now. I've been using FireFox 3.6 on a Windows XP machine, connecting to my MacBook Pro running the latest version of OSX 10.5.
The laptop's native resolution is 1920x1200; within Logmein, I set the resolution to 1024x768. No problem, works quite happily.
However, several times a day (the connection's up for about 8hrs), the resolution will automatically switch back to the laptop's native resolution for no apparent reason. Manually switching it back to 1024x768 causes the connection to hang for a short period, and then disconnect.
When this happens, I have to wait about 30secs before I can reconnect. At this point, most of the time I'll reconnect back at 1024x768, but if it's still the native resolution I can manually reset it.