Very similar issue with my 7+. Was streaming video and it suddenly stopped, even though I had a solid 2 bars of LTE (AT&T). I toggled Airplane Mode thinking to cycle the cell connection.
After turning Airplane Mode off, I could only get "no service". Googling showed this is an issue with some phones.
I tried swapping the SIM card with another phone. Nothing.
I tried resetting network settings. Nothing.
Went in to Apple Store at Polaris Mall at 10am and amazingly as I approached it found signal. 5 bars LTE!
I talked with the Apple folks there for a bit and we decided to see if held signal.
About 5 mins after leaving the mall it went back to 'No Service".
Went back to the mall at 3pm (all day with no service) and it stayed down. Showed the people and they made an appointment for me. Since they couldn't text me they told me to come back in 30 mins.
In the car I watched ti go from 5 bars LTE to No Service a few times.
At my apt time we updated to 10.0.2 and they ordered me a new Jet Black 256gig iPhone in case the update didn't help. The whole time I was in the store (5 bars LTE) it worked fine. Could not get it to loose signal no matter what I tried. Multiple Airplane Mode toggles even worked fine. I left with fingers crossed.
About 5 mins from the mall, with signal around 2-3 bars LTE it started getting VERY slow downloading a new audio book from Audible. I fired up my 6+ and downloaded the same book. 6+ reported fewer bars of LTE but it caught up and passed the 7+ while downloading the book.
When I got to 2 bars LTE the 7+ stopped downloading all together. The 6+ has long since finished. As I watched the 7+ trying to download it suddenly flipped to 'No Service' and there it has stayed. I suspect if got back to a 5 bar LTE area, it would come back.
I suspect the real issue has to do with the antenna in some way as the no service issue only comes up when I'm at 2 bars or lower. Also it seems very slow at anything under 5 bars LTE.
Hopefully the replacement arrives before too long. I've switched back to my 6+ since a phone that only works while under an antenna isn't terribly useful 😟
Other than this, I love the 7+.
One other observation, when it did come back in the presence of strong LTE (5 bars) it does so very slowly. About 5-10 seconds of "searching". When popping a sim card into my 6+ or toggling airplane mode it picks up signal almost instantly.