I am also experiencing this issue on my iPhone 6, running iOS 10.0.1. I have already swapped the SIM card, wiped and reset the entire device, reset my network settings.
Currently, Apple support is sending me to a 'Apple Care technician' to have the HW looked at.
This problem started happening in the morning of Sept. 20th, 2016. I have had two occasions where resetting my 'Network Settings', put my device back on the AT&T network for 5 minutes, then the problem started occurred again, and my phone started 'Searching ...' again, and hasn't stopped.
I suspect this is an iOS 10.0.1 update issue.