Since updating to iOS 6, all of the words I was studying have disappeared entirely. I am now studying only the next words in my list. In addition, the due numbers are falling by 2-4 with each answered item. I wake up with 36 due and they are complete in less than a minute. Should I delete and reinstall the app? Will that make me lose my progress?

It does sound like a fresh sync is in order; I wonder what happened with the data when doing the iOS upgrade. You won't lose any progress. You can go to the account settings and do "Clear Local Data", which will be faster than reinstalling the app.

Xie xie, Nick! That seems to have cleared it up!