It's not a credit card vs. debit booking. MAR doesn't discriminate between the two methods of payment. Seriously it doesn't. It really sounds like a specific property issue. If I were you I'd contact the property again & tell them the bank can see the attempts. If you're willing to do this, i'd conference call the hotel/bank & let them talk to each other & let them figure out the problem (might come in handy to hear the conversation in case you run into it again).

BTW - the Poland example I gave above that friend told me about when we were chatting int'l stuff. Debit card situation. This was after check-in; a bit of a long stay, The Poland bank considered every attempt by MAR to do a pre-authorization as an actual charge, even though it wasn't. MAR's system, if there is a decline, is to attempt to authorize each day. So the 'charge' kept adding on on the Polish side/way over limit. The guest contacted the bank who said the 'charges' would drop off after 7 days, so the hotel (which knew the guest) temporarily switched him to a cash payment so MAR software wouldn't keep piling on. After 7 days, the 'charges' (even though they weren't) dropped & they were able to charge the stay then.

Friend is dealing w/ another Polish guest in the same situation, so it really is dependent upon bank/country.

Cheers.