I have this problem too! And its getting really annoying. If you found out how to fix this please respond.
Screen protector quality may interfere possibly? Maybe something in the cheaper plastics of certain protectors.
Some feedback on cheap protectors vs. dead spots might help. I grabbed a .99 cent one from ebay when I received my iPhone 5, and I have some dead spots sometimes.
It's never consistent, but does seem to happen around the corners and edges more (of course where most interface buttons are located).
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My phone is doing the exact same thing. I literally just got this phone two days ago and put it in a heavy duty case so it wouldnt break like last time. Having my screen not work is very irratating. I cant call, text, use internet, unlock my phone, or just simply type!
In ROME do as the romans do