iPhone 6 touch screen keeps not responding.

Hi everyone.

My touch screen on my iPhone 6 will stop responding for up to 12 hours at a time. It's an intermittent problem that happens for a few hours or minutes then goes away.

I went to the Genius bar at the Apple Store on Wednesday 20th May and they replaced the a new screen, it worked for an hour then failed.

I went to the Genius Bar the following day (Thursday 21st May), waited two hours for an appointment and got a two minute appointment with a Genius Bar worker who said it's a software issue and I just need to re-install the software.

I re-installed the software the issue persisted.

I went to the Genius Bar again today for the third day in a row, and showed that the issue persisted in spite of the new screen and software re-installation and they took the iPhone and re-installed the screen again.

It worked for a while and now I am home and the device still is having the same issue where it doesn't respond. It mostly is unresponsive although will work for a few hours at a time.

According to the Genius Bar guy all their tests say the touch screen is working correctly and calibrated. Can anyone think of any reason the screen is still doing this?