The hardest part of moving to a new service is moving the data over. For a small app, you can do the 'stop everything; copy data; restart everything on new location' thing in a short amount of time without annoying too many people.

If you need to start an app on a cheap or free service, and then it succeeds, you should try to look 2 steps ahead for your move to take into account the data moving problem. The good news with Heroku is that you can just keep adding capacity while you work this out.

There are hosters out there - Engine Yard is well known in the Rails world - who can help you do this if you don't want to run stuff yourself. I've used a company called Bitpusher in the past as well.

At some point though, you will want to bring this in-house as it grows. If only for the cost aspect. Owning your own hardware and employing your own ops people will be cheaper than paying someone else. This is probably a long way into the future for this specific case.