iPhone 6 plus. As with many other posters, I have just developed this issue (as of March 1). Phone was fine, worked fine. Then screen started being unresponsive for short periods, building to being responsive most of the time. Sometimes, this was associated with screen flicker/white-gray lines at the top of the screen. Hard resets did not really help. Called apple support, they had me connect to iTunes, return to factory settings, and reinstall. This did not improve the situation at all. I sent my phone in, they sent a replacement. The replacement is evidencing the same issue.
When the screen does respond, it often responds in the wrong location, selecting something above or below where I was touching.
Can someone tell me if this is a hardware or software thing? The fact that it reoccurred so rapidly with a replacement phone makes me think there may be a software issue, but the lines at the top of the screen sure seem like hardware failing to connect. Is there any way to fix this, besides sending it in again? It can't be that I need a clean install, I've just been through that twice.