I would assume a problem with the company doing the billing.
Typically when an ACH payment is set up, the computers set for billing on the business day before the day they're set to pull the payment. So, if your payment is set to pull on a Tuesday, then everything is set to pull by business cut-off on Monday. If the payment is set to pull on Monday, however, everything is set to go by business cut-off Friday, since Sat. and Sunday are non-business days. If a payment is made before that cut-off, then the system recognizes that the bill has been paid and doesn't pull a payment.
So, lets say that these two companies had traditional ACH payments set up. When you called to update the information, they did not de-link the old ACH, just set up another type of electronic payment. For the first couple of payments, the new payment works just fine because it's pulled before that cut-off, or they set up a one time transfer and it pulled early enough to stop the ACH. Then one cycle the second payment type is either set to pull too late, or was a one time transfer, so the ACH tries to pull. Of course the payment can't be completed because the old information is no longer valid. In my time with MajorBank, I've seen customers go years with an alternative payment type pulling just fine, and then suddenly the ACH, that's been there the entire time, tries to pull.
(And if that was way too confusing, please let me know, because I'm typing and playing kid referee at the same time and probably didn't do a great job of explaining).