I've tried replicating your scenario and I have no problem moving the placemark and having it stay moved.
I open Google Earth, fly to a spot in My Places, right click on the file and select properties, then move the pin with my mouse and click OK.
Then I close Google Earth and when I reopen it the placemark is in the new spot.
I'm running version 5.1.3533.1731. Win Vista SP2
Have you tried all the usual suspects? Clear cache (GE and Browsers), reboot computer, etc.?