Q: Not Syncing movies

Have you looked here:

iTunes: Frequently asked questions about viewing and syncing videos

iTunes: May be unable to transfer videos to iPhone, iPad, or iPod

Where did the movies come from?

What is format?

Any error messages?

Try:

- Reset the iOS device. Nothing will be lost

Reset iOS device: Hold down the On/Off button and the Home button at the same time for at

least ten seconds, until the Apple logo appears.

- Unsync all movies and resync

- Reset all settings

Go to Settings > General > Reset and tap Reset All Settings.

All your preferences and settings are reset. Information (such as contacts and calendars) and media (such as songs and videos) aren’t affected.

- Restore from backup. See:                                 

iOS: How to back up           

- Restore to factory settings/new iOS device.

If still problem, make an appointment at the Genius Bar of an Apple store since it appears you have a hardware problem.

Apple Retail Store - Genius Bar