Q: Ios 9.3.1 no service for cellular data on ipad2 after short period; requires regular ipad restart

Try this

Go to Settings > General > Reset > Reset All Settings

This is not going to Erase any User Data & I hope this will Fix your Issue

You are not addressing to Apple here. This is use rot user forum. The issue is most likely related to your device. I have not encountered any issues with 9.3.1 yet.

Tyr troubleshooting steps recommended here: If you can't connect to a cellular network or cellular data - Apple Support

Do you try

Settings > General > Reset > Reset All Settings ??

If you try this better to Do a Restore via iTunes because it will Update the Modem Firmware

these 2 options will Fix your Issue

While it may have come to light during an update there could be other issues at play. First thing I would try is reseating the SIM in your device and if that does not work get a replacement SIM.

Same here. The SIM works fine in the iPhone, but inside the iPad it will show no connection since the update yesterday. Any ideas what to do? (We did reset the settings and did a recovery today. No changes.)