Sorry to hear about the trouble.
That device is definitely listed as a compatible option with the Square Contactless and Chip Card Reader.
The reader is disconnecting while the app is open in the middle of a sale?
Have you tried connecting to any other device? How is your internet connection in the area that you're accepting payments?
One thing you can try is a hard reset. Hold down the button on the front of the reader for at least 20 seconds. Once you release the button, you should see amber lights.
