Hello Ed,
After doing some research, I found there are a few things you can try. One of them being reset all network settings. To perform this action, please do the following.
On the iPhone or iPad that provides Personal Hotspot, go to Settings > General > Reset, then tap Reset Network Settings.
Another thing you could attempt to do is using a USB tether to your laptop to see if the same thing eventually happens, which would indicate an issue with cell coverage.
Click here for into on USB tethering your IOS device.
Lastly, how good is the cell phone signal quality? How many bars show up?