Never used them but https://www.chargify.com/ is supposed to be a service for this. Of course then you run into the disappearing service problem again.
I work for Chargify and wanted to comment on the "disappearing service problem." Chargify has been around for over 7 years and has been growing and profitable for the last 4 years. If disappearing services is a concern, we do not plan on going anywhere for a long time :)