I have a Windows 7 desktop running Firefox 4. If I remote-desktop (RDP) from another PC into my already-running session, the Firefox window turns black. Flash applications are still visible, if I'm on a tab with one, and I can apparently interact with Firefox normally, I just can't see anything in the window. I'm after an explanation, if possible, and (even better!) a workaround or fix that doesn't involve a different web browser :).
Firefox 4 has changed over to use hardware rendering to improve performance and it is probably this change that is breaking your view of Firefox over RDP.
There is a page at http://www.trishtech.com/internet/disable_hardware_acceleration_in_firefox_4.php that tells you how to disable the hardware acceleration, so it may be worth giving that a try first.
You may well have to close and reopen Firefox for the change to take effect.