Did you rent them on iTunes?
Rentals have time limits : You have 30 days to start watching a movie after you rent it. After you start watching the movie, you have 24 hours (in the US) or 48 hours (elsewhere) to finish it.
Watch your movie rental on a different device:
If you rented the movie on your Mac or PC, but want to watch it on an iPhone, iPad, or iPod touch, connect the devices and sync using USB. When you move a rented movie from your Mac or PC, it disappears from your computer’s iTunes library. You can move the movie between devices as often as you want, but you can have it on only one device at a time.
If you rented the movie on your iOS device or Apple TV, you can’t move it to any other device.
If you rented the movie on your Apple TV, you can watch it on other Apple TVs, however, you can only watch on one Apple TV at a time.