Interesting, is this a U.S. thing? Because I remember reading about attacks on EMV in Europe and they all seemed to boil down to forcing a fallback to magstripe.
After about 3 cycles, it gives up and accepts the magstripe (plus the pin)
Later, before the new card arrived, I tried using the old one again and it worked, so I just chalked the whole thing up to those two stores likely using the same payment processor that was having issues that day or something.
Often it will just deny the transaction completely and the shop queue grows _looong_
What do you do when the chip and PIN fails?