How do I find an app that got lost following upgrade to iO6 I upgraded to iOS6. Something went wrong, and after the upgrade I needed to use an iCloud backup to restore the iPad. 

Although almost all my apps came back, one is missing (it would have been in the backup). It was a simple, free color learning app, but one that meant a lot to my kids. The name was very generic, so I can't find it with Google or App Store search. I tried the  "purchased" tabs on each of my accounts in the App Store, and it isn't there.

How do I find the app, or what happened with it? Could it be missing from the "purchased tab" because it is incompatible with ios6?
New iOS versions never break compatibility with older apps. You could try viewing your purchases in iTunes on your computer. This could be fruitful as the app may have been hidden — to check, go to your account details page (in iTunes) and select "View Hidden Purchases."

Also, consider the possibility that it was downloaded with an Apple ID you haven't thought of. If you're certain it's not on the iPad, you can't find it under Purchased, and neither you nor your kids can remember its name, then it may have been pulled from the App Store. This isn't very likely, though.