You use a 3rd party payment orchestration platform. Spreedly and Very Good Security both offer this and we use them for our business.

I am not familiar with this. What makes them less of a single point of failure?

All they really do is handle tokenization and pci compliance. They're not an active participant in the financial process, basically just a technical proxy. Thus no risk (to them) of charge backs or anything like that, so aside from you not paying your bill, they would have little to no reason to nuke your account.

They're just a tech solution orchestrating (recurring) payments to your payment processors. So they don't have to do the same checks as processors. So they are only a technical single point of failure.

Presumably you have to get certified with SAQ D for actually storing your custopmers payment info instead of tokenizing. Huge hassle.