Well, if the customer with the expired payment information is still using and valuing the service, he will soon realize that he needs to update his payment information without any outside intervention or he will lose access to the service. If the user no longer cares about the service and just forgot to cancel or was to lazy to do so, why not just let him go instead of continuing to sell him something he does no long…
There was this analytics tool called get.gaug.es that i really liked looking at for $6/month. In addition to my existing mission critical analytics apps like mixpanel and google analytics.
I would never have cancelled guag.es but since my credit card switched, i just didn't like it enough to be bothered to update it. A phone call is probably the only thing that would have gotten me to update it. Probably not, but it increases the odds from 0% to greater than 0%