I've cancelled cards previously because merchants were unreasonable or unresponsive. Gyms are one of the worst for this. Cancelling a gym membership is an exercise in torture.
Anecdote: I was in an Equinox gym a couple of months ago, thinking about joining. I saw a "representative" who was happy to give a tour through the gym and explain the costs and benefits. For these sorts of things however I give a fake phone number because I loathe the follow-up calls from such places.
Anyway, at one point while standing around reception where there were 5 or so such representatives standing around the receptionist answered the phone. Someone was inquiring about closing their account. She said they had to speak to a specialist and none were available. What the...? No one else seemed to be with a customer. It just struck me as another tactic to make it more difficult to cancel.
Now for me this would be relatively easy. My company has a corporate membership so it can be deducted directly from payroll and when I say for it to stop, it stops. But honestly I can't condone these hard sell tactics by giving such companies my money.
Cancelling a gym membership should be as simple as a 2 minute phone call or (better yet) clicking a button on a Website (Equinox has a Website where you can reserve exercise bikes no less).
My only experience with dispute resolution was reasonably painful although not as bad as it could be. I ordered something online and the merchant called me to say that price was only when I bought it as part of a package. I said I didn't want it. He said fine. A week later it turned up anyway. I had the charge reversed. They applied it again. I had it reversed (again). I had to send the item back by registered post.
I think the lesson to take from gym memberships and similar fixed-fee for shared usage pricing models is that they create the wrong incentives. Gyms really want customers who pay every month but never come in so they can oversell their capacity. If gyms were pay-for-use you simply wouldn't have this problem. Likewise you could discount memberships for people who come in at non-peak times, etc.
Some point out the "you signed a contract" argument and agreed to those terms. To this I response: people have an innate sense of fairness. People will (rightly IMHO) reject unreasonable terms. If I don't pay my gym membership, I can no longer go to the gym. This isn't like failing to make a car payment.
Unfortunately consumers seem to like monthly fees so you kind of get what you ask for.