I purchased a game on my ipod touch. I restored the device to factory settings last night and when I synced all the apps back, the game is now in the demo version. How do I unlock it ? I hope I don't need to pay for the full version again.

If the upgrade was an in-app purchases see:

iTunes Store: About In-App Purchases

If it was a separate app then redownload that app by:

Downloading past purchases from the App Store, iBookstore, and iTunes Store

go to ur appstore and redownload the full game again you wont have to pay again i promise:)

PES 2012 is no longer available in the US App Store and only on the British App Store currently.

http://pes-2012.en.softonic.com/iphone

That (an app no longer available) happens sometimes.

Your only way is if you have the appt on your computer such as in the recycle bin/trash or in a computer file backup. In that case move it to your iTunes library and sync.

The "purchased" does not save anything. It is just where you go to redownload it (if it is still available) from the app store.

Yes, unless you have it in yur computer's recycle bin or in a computer file backup.

Here:

Downloading past purchases from the App Store, iBookstore, and iTunes Store

Apple says:

It is recommended that you always back up your iTunes library in the event that a purchased item is no longer available on the iTunes Store. For more information about backing up your library, see this article.