lun8t1c

Iphone 6+ purchased Dec 2014

I have experienced exactly the issue described twice - initially mid-May 2015 - they replaced the screen, and Jun 2015 - they replaced the whole phone - no questions asked. I have had no issues since - though at times if my fingers are damp the screen may not react as expected. 

I have always had a quality case and screen protector on the phone - careful not to bend it by not leaving it in my pocket when I sit down.
 
There is clearly an issue of some type that effect a small proportion of phones, and the fact that after the initial repair not solving the issue long for more than a month, they were so prompt at replacing the phone, someone knows there is an issue and has done so for at least a year, whether they knew the actual cause or not.