iPhone screen unresponsive
I have an iPhone 6 (with the latest iOS updates) that is one year and four months old. From February, it has started to become unresponsive to the extent that sometimes it is impossible to get anything done. I need to switch it on and off several times to for example get text message written. Everything else works, but the screen just doesn't respond to touch.
I called Apple Support, and they were very nice and took me through diagnostics and all. I reset the phone a couple of times, set it as new, used the backup to retrieve the data but soon after these very laborious processes the phone got back to its bad habits of non-responsiveness.
I am puzzled. The diagnostic showed no hardware problems but a few software crashes. So, the iPhone should be good as new, but I am stuck with this issue.
Does anybody know how to fix this?
iPhone 6, iOS 9.3.1