Taking swipe payments with a mobile device is really handy, but if your connection drops out, it can quickly become a disaster. You probably won't get a lot of sales jotting down card numbers on a scrap of paper, but Square has a solution. The new version of Square Register for Android adds offline mode so you can still swipe cards without a connection.
Previously, the app would refuse to take payments if it was unable to process them on the spot. That's pretty much the behavior you'd expect. The new functionality allows the app to cache the transaction information locally when there's no data connection, then process it the when connectivity is restored.
Offline mode can be enabled in the settings and will save transactions for up to 72 hours (they expire after that). There is also an optional transaction limit for offline mode, which you might want to take advantage of. It would be a bummer to lose a ton of cash because you don't get connectivity back in time.