Can a business come back 3 years later and ask that I PROVE them to pay 3 years ago?

I bought products / services from a business 3 years ago. Under the arrangement, I was paid half up front, and the other half after the goods were delivered / services were rendered. I charged for it with two separate credit cards. Three years later — I asked for more services and entered into a new contract — and paid half in advance, and the other half would be compensated upon receipt of the services. Now they say they can’t trace my final payment from the first contract and they want me to show that I paid it (three years ago). If I don’t pay them (twice) for the original services, they’re not going to complete the second contract-and I’m losing my down payment. I have never been contacted about any past due amounts, or overdue amounts, three years ago or at any point after the initial agreement. Would they really do this-three years after that?