I had this same problem for a few weeks with my 6 Plus. I missed a lot of calls that I couldn't answer. I thought it was dryness on my fingers at first (super dry climate), that the screen couldn't "see" my swipe. This delayed my diagnosing the real problem. It kept getting worse and eventually I had to get the phone replaced on warranty. The cause was a bent screen, which wasn't at all noticeable - the "non existent" bendgate problem. Also, when it went into freeze mode, the screen greyed out just a bit. I'd restart numerous times, and if it came up black (rather than dark grey), I could access it again.
My less than one month old replacement iPhone 6 Plus now has a similar problem - it becomes non-responsive and I am unable to answer calls or access apps. If I flex it just a bit, hold the center and push the top right corner down, it works. Otherwise, it's non responsive to touch.
A day ago, the freezes have increased, and a band of white/grey noise creeps up and down from the top of the screen, 0% to roughly 10% of the screen. Then a few hours later, it did something I'd never seen before - started switching through apps and screens on its own, randomly, without the phone being touched.
This is a very serious problem - perhaps a replacement program is called for. My iPhone 6 Plus will be out of warranty soon, as will millions of others that didn't buy Applecare when they purchased their phone. What happens then?
