As you've found it seems to me to be an overheating issue, or at the very least a downclocking issue. Dell's come out 3 times now -- new MB, new fans, new processor but the issue still exists. I've used A17-A20 bios, problem still exists across the board.
The one thing I've done that keeps it stable is to use the RightMark Clock utility (free download) which allows you to keep the throttling at 100%. This will affect battery performance but I don't have the issue out of the dock typically. Hopefully they'll find a permanent fix soon. I also had someone recommend disabling speedstep in the bios which also seemed to work however that also negatively affects battery life when not plugged in so the RMClock utility works better for me. When i'm docked and it starts downclocking I just fire the app up and the issue goes away...
Good Luck!
Here's a good link I've been following on the issues...
Dell Latitude E6400 - Overheating issues with minute tasks such as playing flash videos for extended periods? - DELL COMMUNITY