One reader spotted a solution from Apple's support forums that shows how to get around the issue:
Go to Settings>General>Date and Time>Set Automatically>Off. Set the date one year ahead. Try to [update the apps again or press the button from Passbook]. If you get an error message, go back to the settings. Correct the date and time (set automatically) then go back and try [again].After switching the date, we were able to successfully connect to the Passbook section in the App Store. A few other readers also reported success with this technique.