But ultimately we exchange at least a few emails with every cancellation and try to understand exactly why we were no longer addressing their need. 99% of people are extremely willing to help out here.
Also, Exit Interviews: http://www.extendslogic.com/business/jobs-to-be-done-cancel-...
Any service which lets me sign up online but not cancel online is incredibly distasteful.
Personally, I am usually happy to give feedback to fellow business folks, and I wouldn't be offended if someone politely asked for it from a service I was cancelling. However, if a single reasonable action to cancel and no further contact resulted in my card being charged because I didn't play along, that service should not expect a happy outcome.
We respond with: "Bummer to hear, but happy to take care of that for you. Anything we could have done better?"
Then that usually sparks a longer conversation, but if we don't hear back within 24-48 hours, we just go ahead with the cancellation.
We're also very generous with refunds and certainly wouldn't keep someone's money just because we delayed the cancellation a day or two. That's just silly.