I Have this same problem on iPad 2 since the 9.3 update. I haven't found a solution but I have found a way to get the cellular network back. But if you power off and then power on you will find it gone again and you have to redo the following work around.
1. power off and remove SIM card. Then power back on and it will ask for SIM card. insert sim and it should find the network. This is simple but if you have a case it is a nuisance to keep pulling it apart.
second workaround.
1 Go to settings and turn cellular (mobile) data OFF.
2 Turn Aeroplane mode ON.
3 Power off iPad.
4 Wait about a minute. (Not sure if this is absolutely necessary)
5 Power iPad on.
6 Turn Aeroplane mode OFF
7 turn Cellular Data on.
you should then see a cellular provider box pop up under the Cellular Data box and the it should search and find your network.
this works on the iPad 2 and hopefully other iPads.
I Noticed heavy battery drain under 9.3 and when I ran my iPad in the No Service condition, battery usage improved dramatically.
good luck.