Try the standard fixes:
- Reset. Nothing is lost
Reset iPod touch: Hold down the On/Off button and the Home button at the same time for at
least ten seconds, until the Apple logo appears.
- Restore from backup
- Restore to factory defaults/new iPod
What are you expecting? Does the app reopen at the same location as when you left the app?
I tried resetting my iPod like you said but that didn't make any difference so I will try restoring it. I'm expecting it to reopen the app where it left off whilst it's still running in the bar (when you double click the home button). My sister also has an iPod touch 4th gen and hers will open where it left off, although she has not updated hers to 5.1.1 so I was wondering if it was to do with that.