Yes, I got the first iPad mini (original model non-retina) and about 10 mos later, it started to have this problem - tried resetting, clearing out all the Apps, etc...nothing worked. I went to the Apple store and within two minutes they replaced it with a new one (same model - non-retina). I considered that excellent service, the new replacement worked perfectly. Unfortunately it is now about 10 mos later and the new replacement is having the same problem. Neither unit had any water damage whatsoever, nor were they ever dropped - yet but both are having the same problem.
The original warranty has expired and so there does not seem to be any recourse from Apple. And if I pay for a repair - it seems it is likely to develop the same problem.
I read online that some people suspect that somehow condensation forms inside when the temperature changes from cold to hot and that is what is causing this problem. It was suggested in an online forum to try heating the unit under a blow drying - I guess to evaporate the moisture. That seems far fetched and very risky. I have not tried that and i do NOT recommend it. However, I guess if you are prepared to throw away the unit anyway, then it may be worth a final gamble.
I am curious if anyone had found a cause for this problem or a fix?
The real question for me is - should the next tablet I buy be an apple product or another brand?