I'm having the same problem. My wife and I ordered iPhone 6s through AT&T at the same time, received them the same day. They started having problems where the data connection would just stop working, and the "4G"/"LTE" logo would be there sometimes, sometimes not. Rebooting, restoring, network connection reset -- none of it was helping. So I sat on the phone last night with an AT&T tech support rep --- she resent our activation codes, and that immediately solved the problem for my wife and I's phones. I was happy, because the last thing I wanted to deal with was replacing hardware on phones that are in this short supply.
Now tonight my iPhone's data connection drops, just as it did yesterday. My wife's continues to work. I reboot, and it comes back, but only says 4G. I go into the settings and toggle airplane mode on and off -- LTE logo comes back. Great -- when will this break again?
This is just a horrible impression I'm having of these new phones. I don't know whether its the hardware, AT&T's network, or what, but the net experience is very anti-Apple. And that's for someone like me that has been using Apple computers since .. oh ... 1980? I tend to give Apple a pass on a lot of things, but this is just a horrible experience.
The worst part is not having the tools to determine what is wrong, like I could with a desktop computer. I can't go to a shell and look at logs, or look for a stuck process, or crashed process/driver, or what have you. I just have to think, "this is a buggy piece of hardware/software and was rushed out the door."
My best guesses are either (1) it's a software issue, and the data handling process is crashing -- maybe IOS 8.0.2 didn't complete resolve the issues in IOS 8.0.1 with regards to connectivity; or (2) it's a hardware issue, and AT&T is shipping phones that have flakey SIM cards.