Credit card swipers have a rechargeable battery in them. If your swiper stops working it could be that you need to keep it plugged into your phone for awhile to charge the battery.
If the problem persists, you may need to unplug and plug the swiper back in.
Other things to try:
If you leave your card reader plugged in all day, only plug it in on the "shopping cart page" with the totals on it BEFORE clicking next.
To clear the problem when it just won't connect to the reader, you may need to refresh your app. To do this...
Double click the iPhone/iPad button on the device (the actual hardware button). The screen will show you smaller pictures of the apps you have loaded. Swipe up on our app to take it out of memory. Restart the app and it should work now.
Click the button on the lower left of the device. The text "Close All" will come up. Click that message. Re-launch the app and this should solve the problem.