Is there a reason why this would happen? I almost want to upgrade to iOS 6, but I love the functionality.
It will only add videos I've purchased, like music videos that came with a terrible Kid cudi cd.
I've never seen it trying to uninstall Cydia - I have almost all iDevice models (I'm also teaching iOS programming so I need that many models), the majority of them jailbroken and regularly synched (videos too).
I've purchased several iTunes Store movies but never had any problems you explained above.
A solution is, as long as you only want to watch music videos (which aren't copy protected and consequently, as has just been explained, can be played back in third party players), giving a try to a third-party player.
Should you want to stick with DRM'ed videos, circumstancing the entire synching is certainly possible on JB'n devices. Give a try to just copying the DRM'ed M4V files to your device by simple file copying anywhere. Fire up iFile, navigate to the file, tap it and select "
Video Player". They will be played back - even DRM'ed ones.
Note that
- the latest version of iExplorer 3.x and the Mac version of iFunbox can't copy videos to the device
- SynchPod (which used to be a VERY good app for multimedia transfer in both directions) doesn't seem to work with the ML + iOS 5.1.1 combo.