Touch controllers on iPhone 6, 6 Plus failing in specific way for some users
A handful of users of the Apple iPhone 6 and 6 Plus are reporting manifestation of display aberrations and inconsistent touch functionality -- and a screen replacement doesn't fix the problem.

The problems with the 2014 iPhone 6 and 6 Plus generally start with a small patterned band at the top of the screen of afflicted devices, according to the Apple community support forums. As time goes on, the aberrant band sometimes extends further down the screen, and touch sensitivity and device response to the touch gets progressively worse.
iFixit has collated reports from component-level repair shops from around the U.S. that have seen the problem. One vendor claims to repair about 100 iPhone 6 and 6 Plus models a month exhibiting the problem. Others report dozens.
AppleInsider has spoken with a screen repair chain that performs repairs on about a thousand devices a week that confirmed seeing the problem, with "a few [iPhones] a week" that enter the shops exhibiting the issue.
Third party repair shops have traced the problem to the chips that translate the user's touch to information the iPhone can use. These controller chips are sometimes failing outright, and in other cases the microscopic solder joints connecting each chip to the motherboard are breaking, causing the progressive failures.

While a single root cause of the problem has yet to be determined, the problem may be related to the "Bendgate" issue from 2015, where the large and thin iPhones were warping as a result of force applied by users. The increased incidence of flexing of the case because of the larger surface area may be exacerbating the problem over time, and causing more solder joints to break.
Apple may have been aware of the potential for a problem with the touch controller when it designed the iPhone 6s family. The touch controller has been moved to the display assembly. In conjunction with overall frame strengthening, the migration appears to be protecting the controller chips' solder joints from the flexes the iPhone 6 endures because of its size.
Prior to the iPhone 6, the touch controller chips were reinforced by a metal electromagnetic interference shield as well, protecting older phones from the same problem.
Apple's solution at this time is to replace a device that has failed in such a fashion. Third party non-warranty repair shops specializing in micro-soldering can replace the touch controllers that are failing as well, but this invalidates any Apple warranty.

The problems with the 2014 iPhone 6 and 6 Plus generally start with a small patterned band at the top of the screen of afflicted devices, according to the Apple community support forums. As time goes on, the aberrant band sometimes extends further down the screen, and touch sensitivity and device response to the touch gets progressively worse.
iFixit has collated reports from component-level repair shops from around the U.S. that have seen the problem. One vendor claims to repair about 100 iPhone 6 and 6 Plus models a month exhibiting the problem. Others report dozens.
AppleInsider has spoken with a screen repair chain that performs repairs on about a thousand devices a week that confirmed seeing the problem, with "a few [iPhones] a week" that enter the shops exhibiting the issue.
Third party repair shops have traced the problem to the chips that translate the user's touch to information the iPhone can use. These controller chips are sometimes failing outright, and in other cases the microscopic solder joints connecting each chip to the motherboard are breaking, causing the progressive failures.

Location of the touch controllers on the iPhone 6 motherboard, photo by iFixit.
While a single root cause of the problem has yet to be determined, the problem may be related to the "Bendgate" issue from 2015, where the large and thin iPhones were warping as a result of force applied by users. The increased incidence of flexing of the case because of the larger surface area may be exacerbating the problem over time, and causing more solder joints to break.
Apple may have been aware of the potential for a problem with the touch controller when it designed the iPhone 6s family. The touch controller has been moved to the display assembly. In conjunction with overall frame strengthening, the migration appears to be protecting the controller chips' solder joints from the flexes the iPhone 6 endures because of its size.
Prior to the iPhone 6, the touch controller chips were reinforced by a metal electromagnetic interference shield as well, protecting older phones from the same problem.
Apple's solution at this time is to replace a device that has failed in such a fashion. Third party non-warranty repair shops specializing in micro-soldering can replace the touch controllers that are failing as well, but this invalidates any Apple warranty.
Comments
Of course, I am out of warranty already but truth be told I have not tried to take it in yet. I feel that I can last till the new one comes out.
It is extremely frustrating.
https://www.apple.com/support/exchange_repair/
This issue is definitely a result of the phone getting bent after over a year of usage without a cover. I now use a cover with the replacement device.
9TO5Mac is calling this “widespread” and iFixit is demanding a recall from Apple. See how this works? It’s already started. Meanwhile the Galaxy S7 has been found to be less water resistant than touted, the Gorilla glass scratches easily... and nobody gives a shit. Not a rat’s ass.
If you've had the problem, keep your documentation, just in case.
The real message is get the two year warranty contract. These devices get a lot of abuse [including bending] and for 2 years the device is under repair warranty [and as I recall some user abuse repairs, water damage, for low cost]. This is a pretty good deal considering the cost of the device, the likelihood of a problem given its heavy usage, and feeling of comfort/security.
It would be nice if Apple offered a three year warranty, but I suspect the durability makes this an expensive option for them unless we were wiling to pay a steeper extended warranty price. Also, the end of life period is shorter and like the Macs Apple will not repair after end of life.
It started happening about 6 months ago but I couldn't find anything about it. Unfortunately my phone is out of warranty by about a year so I'm not sure what I can do other than lean on Vodafone due to the Consumer Guarantees Act in New Zealand.