RDP can maintain the session if you use the console (mstsc /admin), unfortunately it does not solve the issue of FG freezing when you close your connection. So the only solution when I log back is to kill FG and re-launch it. That's annoying especially since the DB becomes corrupted and cannot be auto-recovered too often.
The only solution I have found to prevent DB corruption is to put back FG in window mode instead of full screen before I quit the session. This does not prevent FG from freezing, but it does close far more nicely by using the windows closure than by killing it with the task manager (only solution if full screen).