It should show up normally. Before your next show, test it out at home. If the register doesn't show up, close the app completely and try launching it again. If it still doesn't work, you might need to delete and reinstall the app. No accountinformation is stored within the app, so you won't lose anything. You'll just need to sign in again.

If you're able to process a few cards offline and then suddenly can't, don't delete the app before going online as you will lose the card information that you did get. If there's any way for you not to run in offline mode at fairs, I would encourage you to try it, as offline mode isn't particularly safe. You end up being responsible for denied cards, etc. https://squareup.com/help/us/en/article/5095-process-payments-with-offline-mode