Not sure it's only a Visa problem.

I use an American Express Centurion card, which comes with a 2nd card
in my name (to separate expenses).

I never had problem using the 1st card (main card), but the 2nd card is
usually refused in Paris as beeing "not valid". I checked the card at the American Express office, they could read in the magnetic stripe without problem.

It's possibly a software problem in the terminals reading the card, and
checking the formal correctness of the information recorded on the
magnetic stripe (check numbers etc.)