However, it seems like it is a bug in iOS 8 and many users faced such problem. Since I have got my iPhone 6 Plus I have rebooted it several times, even Reset Network Settings. None of the iOS 8 software updates have also magically fixed the issue.
However, I’ve figured out a workaround to answer the call in this situation. When I get a call and I am not able to answer it when I tap on the Accept button, I press the Sleep/Wake button, and it seems to do the trick sometimes. Ideally, the Sleep/Wake button should silence the call (so not a great solution if you want to silence the call), but in my case it helps me answer the call. This trick doesn’t work all the time.
I haven’t tried restoring my iPhone. But if you’re facing the problem then that could be the last resort to see if it helps. Some people have said that restarting the iPhone seems to help temporarily, but they face the issue again after some time.