I had this infuriating problem and after devoting a lot of time I think I've managed to resolve it.
It seems to be a problem that is not just unique to Revit. Everything seemed to be pointing in the same direction, a registry problem associated with the MRU files.
I've just recently completely blitzed my registry with a couple of registry fixers/cleaner applications. I don't like using them too much but desperate situations call for desperate measures. Specifically I ran Systweak Advanced System Optimizer v2 and VCOM Fix-It Utilities 7 Professional. First a restore point was created and then I ran ASO which picked up about 300 issues. Then I ran Fix-It and it listed over 1300 issues which were cleared. Fix-It recommended running again as the first repair run would reveal more issues. I ran it again and this time there were over 1700 issues which were again cleared. I re-ran it a third time and this time it returned only 5 problems.
With such a drastic change to my registry I was sure I'd run into problems following a restart. But alas, thankfully not. It could be my imagination but things seem to be a bit faster. But the best thing of all was that upon starting Revit and clicking on the File menu, it just dropped down with 4 MRUs listed. If you haven't had this problem then you cannot imagine what joy that brings.
This cure is somewhat risky, but for me it was worth the risk and fortunately I came out smiling. I used ASO and Fix-It because they came joint top in a Registry Repair Review. ASO has a 30 day free trial and a colleague has (and swears by) Fix-It. I'm not sure which one actually did the deed but if I had to guess I would opt for Fix-It.
Hope this helps even one of you guys, it's a truly frustrating problem, and if it misbehaves again I'll let you know.
Tripe