Theoretically, SIM cards can fail. It doesn't happen often, but it can happen.
The real question I have is are you losing all mobile service, or when you lose mobile data, can you still make/receive calls and texts? That will most likely tell you where the real failure point may be. If you lose all service, it might be worth getting a new SIM from Airvoice and having them transfer the account over to see what happens.
This said, it's worth noting that the biggest failure points involving SIM connectivity with a handset is the crammed tiny spring loaded SIM contact pins in the phone itself with a side-load SIM slot. You can kill a phone by damaging five cents worth of contacts, and you do it through repeated removal and re-insertion of the SIM card. Yet another poor mechanical design choice of the iPhone, unfortunately, though Apple isn't alone in this foolishness. SIMs just aren't really designed to be frequently moved and removed, especially with side-load nano SIMs. But this is a worst case assumption of something that is putting the diagnostic cart before the horse on, so to speak....
...but, there's your starting point. Is it data only, or all cell services? If it's data only, it's most likely going to be a problem with the phone itself if a hard reset didn't fix it. Whether that's software or hardware, is a whole other kettle of fish. If you lose all connectivity, it's worth trying a new SIM to see if it fixes the issue, but if it doesn't... we're back to the phone and possible hardware issues.
We go way back on these forums, and I know you love your iPhones... but if it eventually turns out to be hardware and if it turns out to be an expensive fix, maybe consider an Android handset next go around? The Moto G4 Play is a solid device for the money. User replaceable battery, well designed, decent battery life, you can use MMS with Airvoice on it, has mainstream third party Android build support if you ever stop getting official OS updates, cheap... :)