Square register is simply using the internet connection that the hotspot provides to the iPad (or whatever device you use). Square Register doesn't connect to the hotspot or maintain the connection the Device does. So if you are losing the connection there could be a timeout period of inactivity that your device then drops the connection due to not being used, or the hotspot itself disconnects the device after a period of inactivity. Or you don't have a stable connection (distance to the hotspot or interference) and the device naturally disconnects.
I have some luck using my personal hotspot from my iPhone to another iPhone but it disconnects very frequently. Sometimes it stays connected for 30 minutes other times it seems to disconnect when the device screen goes to sleep.
