Unfortunately, when they released iOS 4.2, Apple lowered the power requirements (usage? ability?) in that port. So, now, it is tremendously underpowered and will not run a lot of things, as you've seen.
There is no fix for this. All I can suggest is to use another method of getting those videos to play on your iPad, such as cloud storage or via iTunes.
Sorry to not give you a more happy answer.
Marilyn