Another time, I had a service continue to try to bill me monthly for 2 years. I just let it keep saying "your order is about to ship" and "there was a problem with your card". Eventually, they found a way to charge me (I'm really not sure how) and had an order go through, after which I cancelled through an option buried in their website.
1. You get a virtual card number to use for subscriptions
2. We detect recurring charges
3. We send you a text 24h before any refills
4. If you reply 'skip' we block the next charge, if you reply 'cancel' we cancel the card entirely
So the gym just lets them collect a balance and then threatens to send the bill to collections if it's unpaid.
If I were in that situation, I suppose I would open a new account just for that purpose, turn off overdraft, and transfer money into the account as needed.