What kind of fraud does it sound like? I gave my credit card to the merchant and said they could charge it for auto-renew, but that doesn't seem to put me under any obligation to make sure the card is still valid next year - credit cards expire or get canceled all the time. The merchant is free to cancel the subscription if the auto-renew fails.
Contract law in general does not prescribe that the contract is automatically terminated with no obligations if some payment doesn't arrive. The method of payment is pretty much orthogonal to any obligation to pay and the continuation of the contract.
The contract may stipulate that the merchant is free to cancel the subscription if you don't pay for whatever reason (the card expires, the card does not have money, you chose to pay in cash and didn't have a card, whatever). However, the contract can (and usually does) stipulate that the merchant is not required to cancel the subscription in case of non-payment, and in that case the contract is valid, they owe you service and you owe them the contractually agreed payment.
On the other hand, contract law generally would assume that the subscription is cancelled if you sent them an unambiguous request in writing even if their standard process flow (e.g. requiring a phone call with a sales rep convincing you not to quite) wasn't followed - if you've sent a letter than that and stopped paying, that should be appropriate in most circumstances.
For anyone wondering - no this definitively isn't fraud - no it will have no impact your credit (there isn't even a mechanism for this to happen), nor will it get debt collectors after you (you don't owe a subscription continual payment, failure to pay only means they can terminate your service).
I have encountered similar tactics from a popular VPS provider. Set up your account to auto-renew, send the invoice to collections if they can't charge you, instead of just canceling the service. Infuriating, to the point where you'd think they'd be more concerned about driving away future customers.
Why would it be fraud? I paid for the service when I used it, if the business makes it impossible to cancel a subscription or makes you go through endless hoops to waste your time, that's on them. After I stop paying for it, they'll just stop providing me the service.
If you signed a contract for X amount of months, then I get it, you have to pay, but I always do month to month at the gym, they still make it impossible to cancel.
This is not fraud at all. You could just as easily file a dispute. You're under no obligation to continue allowing a company to charge you a recurring subscription that you do not wish to continue with.
Cards stop working due to fraud or lost cards all the time. Businesses must accept this as a fact of life. Forcibly dunning is a malicious business practice.
Credit cards expire all the time, if I had an interest in ensuring payments flowed I would have given you an updated credit card... which I'm sure would be easier than cancelling.
For what it's worth I've never had trouble canceling anything I've subscribed to.