Sounds like a case for the logs... I've always found the Live Mesh rdp to be slower than normal remote dekstop (hence I use unfortunately am stuck with normal RDP, which is more of a pain to configure, but has the speed benefit), but I've always found it reliable.
Collect the logs from both machines and send them into
lmprev@microsoft.comTo collect your logs:
1. Click Start.
2. Select All Programs and look for the Live Mesh folder.
3. Click Collect Live Mesh Logs.
4. Your logs will be bundled together in a cab file now located on your desktop.When they find a fix - post it back here for everyone to read :)