iPad Touchscreen unable to work sometimes

At random times, the iPad touch screen stops working. No presses or swipes on the scren register. However, I can still use the home button to minimizes apps and the lock button to lock the iPad etc.

The strange part is, after leaving it for a while (could be anything from 10 minutes to two days) it starts working again. I'd say I get about 20 minutes use out of it before it goes back to being unresponsive.

And before someone gives me the copy and paste answer of "press home and lock for 10 seconds", you would not believe how often I tried that. Sometimes it works after 5+ times of trying that (no exaggeration) but most of the time it does not. I even reset it to factory settings two days ago, but still experience the same problems.

This has happened through every iOS I've had from 6+.

It's an iPad 2 Wi-Fi 16GB.

Any help or advice would be appreciated, thanks!