Searching for network

#1
Someone please help. I have an iPhone 6 AT&T that will get on a network and stay on it for a day or two and then drop. Then it goes into constant searching mode. I was on a two week work trip where I was flying to multiple places and the problem would persist. The solution that worked temporarily was resetting the network settings but that would only work once at each location until I moved onto the next. I have since reverted to a 5. Today, I swapped out the sims and reset the settings again and lo and behold, it captured signal again. The pesimist in me is waiting for it to drop again. I took it into several apple stores and they all pretty much told me something is wrong with the phone and all they can do is offer a replacement at a cost. In my mind, it can surely be fixed if it works temporarily. Anyone have any ideas? I have upgraded to the lastest software and installed all the carrier updates. Any help is very much appreciated.