Since the commentary to Reg E 1005.6 allows for the fact that a consumer could write their PIN on the card and still not be liable for unauthorized transactions. The mere presence of Chip and PIN is not sufficient evidence to conclude that your customer authorized the transactions. There could be a family member or friend performing shoulder surfing and obtaining the PIN and later taking the card and putting it back, or the customer could be engaged in a card cracking scheme and giving the card away in exchange for payment and later claiming fraud. There is not enough evidence to make a determination.
Regardless of the number of claims a customer has made, Reg E requires that we investigate and determine whether or not a the customer authorized the charge. We may attempt to obtain video surveillance, copies of receipts, review transaction patterns or undisputed claims, etc.
The operational question here is, "Why does this person still have a card?" A debit card is a privilege, not a right, and the bank may be well advised to limit this customer's opportunity to cost the bank additional money.