Ever since I updated to 11.3 I have had this very same problem. I don't use the lightning headphones, I use the AirPods with my iPhone 7 Plus. The sound just stops, but the Music App shows my headphones as connected and as if it was still playing. At the beginning it only occurred occasionally and during the first 20 seconds of a song. But now on iOS 11.4, I feel like the problem has worsen. There was a point where it would do it on every single song and it is beyond annoying.
I have noticed now that it only happens when the phone has been just locked. I have also noticed that when charging the iPhone while playing music, the iPhone does not stay awake and now it locks, which it didn't use to happen before, hence causing the problem.
The issue has also extended to other Bluetooth devices, or at least I just realized about it. So now I am assuming this has nothing to do with the AirPods, but it's more like a Bluetooth connectivity issue. Somehow when I lock the phone the signal is interrupted, or I don't know.
A quick solution on the fly for me is to invoke Siri and immediately close it. That brings back the sound at once, but I hate to do it every time.
I have not tried the full restore like you guys, I was avoiding it on purpose because I don't really want to do it. I don't even like to sync my phone, but I don't see any other option left.
If not Apple, I hope that at least one us find a solution.