How will the money "dry up" and leave them (AMC) unpaid exactly? It's a debit card, the money is exchanged on an immediate basis. (Same as a cash purchase.)
The company has been around since 2011 and has been selling the movie pass for a number of years now, just at a $50/$60 monthly rate.
One thing they have going for them, in regards to theater support, is that the research is showing that people who use movie pass are likely to spend 125% more on concessions than those who pay normal ticket prices. In reality, theaters typically make more from concessions than from their share of ticket sales. The more butts in seats and the more those butts are buying sodas, popcorn and candy at ridiculously high profit margins, the more the theaters will make. I could really see AMC change their tune shortly.
But from a legal perspective, unless they're willing to deny purchases on Mastercard, they can not deny Movie Pass.