Lost movie rental on my iPad

Check and see if it is still on iTunes. I'm pretty sure, I read about this the other day, that you can only transfer the rented media file to one device. Meaning, if you don't transfer it from your computer to your iPad, it won't automatically show up on your iPad. Once you transfer it from your computer to your iPad, it won't be on your computer. Also check to confirm it has downloaded. Sometimes, you can purchase it but the download doesn't start.

Videos App>Rentals

You cannot sync rented content between devices. It stays on the device where it was originally rented.

Read this:

http://support.apple.com/kb/HT1657

Can I play my rental on more than one device?

• If you download a rented movie on your computer: You can transfer it to a device such as your Apple TV (1st generation), iPhone, iPad, or iPod if it’s a standard-definition film (movies in HD can only be watched on your computer, iPad, iPhone 4 or later, iPod touch (4th generation or later), or Apple TV). Once you move the movie from your computer to a device, the movie will disappear from your computer's iTunes library. You can move the movie between devices as many times as you wish during the rental period, but the movie can only exist on one device at a time.
• If you download a rented movie on your iPhone 4 or later, iPad, iPod touch (4th generation or later), or Apple TV: It is not transferable to any other device or computer.