iPhone screen periodically unresponsive My iPhone 6 had a problem where the screen stops responding to touch for a period of time. It always becomes responsive again after a while, although sometimes it requires a power button cycling. 

For reasons I cannot explain, I feel this is a software issue. It happens in all apps, but it seems to have a sort of schedule. 

Has anyone else an anything like this?
No, not as a general issue across all apps.

Some apps such as for example Safari may be "slow to scroll" (for example web pages that have Javascript scroll handlers that do not declare themselves as never calling preventDefault() can be slow to scroll).

However, if you see this as a general problem across all apps, and you have to powercycle the phone - it sounds that a hardware problem is likely.

If the phone is still under warranty - take the issue to Apple Support. If it is not, you could still try Apple Support.