Ask HN: How to do a major back end refactor?

Some time ago I've partnered up with a guy who had an app and backend developed by a software house. It's a niche SaaS business iOS app + RoR backend.

The iOS code was total trash, the backend was somehow working but not reliably. So I set to remake the iOS app and bugfix the backend. Now a year later, we have about 100 paying customers and would like to develop futher.

Now, I'm not a RoR specialist, but I can tell that the API was not architected properly, the performance is poor. Everytime I have to do bugfix or extend backend I feel like walking on a thin ice, even though I've a staging server.

What do you think would be the right way to grow? We have a lot of features to implement, but we also need to provide a stable system for existing users. I feel like this system is too rigid and just bad to continue developing on.

Have someone gone through something similar? Is there any backend technology I should check? (maybe something abstracted like Parse used to be?)