Hello I_drilling,
I own the exact same iPhone (iPhone 6s Plus) and I am also experiencing the same problems with it.
I found out that if you shut down your iPhone, remove the SIM card via the SIM card needle (0.8mm), and re-assemble the SIM card, and restart the iPhone.
If it doesn't work, check your SIM card, see if there is any visible damage, try it on another phone (if there is one available) It might be the SIM card's problem, and if so, you probably should find your cellular data carrier's service provider and replace the SIM card with a new one.
If it works but the data service fails again repeatedly, there might be a problem with either your iPhone or your SIM card. Again you might want to get a new SIM card, and if that still doesn't help you might want to check your iPhone or bring it in for support.
Again, that is my way (or the way I figured) and you should check:
If you can't connect to a cellular network or cellular data - Apple Support
Hope that can solve your problem!
Best Regards,
CatTM Tech