Cellular update failed.

Unfortunately this appears to be your problem -->If you see a Cellular Update Failed or Apple Pay Not Available alert after iOS update or restart - Apple Support You need to contact Apple support or take it to an Apple store to resolve it. Genius Bar Reservation and Apple Support Options - Apple

If it was an issue with the cellular modem it would never work. The fact that it works sometimes means that there's probably a different issue. Go to Settings/General/About and look at the modem firmware version. If it is not blank this is not your issue.

Have you checked to see if this applies to you? -->iPhone 7 Repair Program for "No Service" Issues - Apple Support. I suspect it doesn't either, as this problem isn't intermittent - it just stops working altogether.

What is a possibility is a local Verizon network outage; that would explain the intermittency.

It's also possible that it's a loose, but not broken antenna connection in the phone.

Hi, so I’m having the same issue where it keeps saying “searching” or “no service”. The modem firmware version is blank for me.... not really sure what I should do. It worked only for half an hour but it my phone was also restarting by itself. Weird thing is it’s only today... help?

If I were you, I'd take it to Verizon for assistance.