I use a bank card and try to always pay as debit. There is no limit to the number of transactions, although they may limit you to a maximum amount, $100 or so per day. Some pumps won't accept debit. For those, I select the credit option, but can only use it 2 or three times as you say. Some pumps will only take credit cards, not debit cards used as credit cards. For those, I reserve my actual credit card, but I would not feel badlreporting the card reader did not work on those. As a last resort, I use the Valero Pay app, although not all stations are set up for that. And of course I bring cash.
In your case it may be just those stations that don't take those cards. I often run into a string of stations that want credit only. Maybe it has something to do with the area's payment network or similar ownership of the stores.