Having the very same predicament with Three in North-East England; a couple of weeks ago all was well.
It looks as though resetting the network recalibrates according to your current location; move a couple of miles away, the signal source will change and 4G will disappear, never to return. I've tried it in a few different places.
It was unclear what the source of the issue was; I updated to iOS 10 and then a few days later got an iPhone 7+. But it seems to be the software (I hope). There are no current carrier updates from Three; possibly something is to be included in iOS 10.1 or an earlier update. I suspect a new phone will exhibit the same symptoms (but would appreciate an update).
It’s compromising a non-cheap all-you-need data deal; to get the best out of it one needs 4G.
What’s most disappointing is that this is the sort of thing I left Windows for (now drive a MacBook), the updates that break things. But researching this, I find it’s happened with every single major update since 4G became a thing. Poor show. In passing, the phone notifications are a bit rubbish at updating too (hello Windows Mobile?), but that I can live with for now.
Rob
(also Roberto, btw 🙂)