If someone else's server provides a critical service for your app, and your livelihood depends on it, you're probably better off to operate your own server rather than to outsource it.
Suppose branch.io fixes their current problems, but next year goes totally bankrupt. How would that affect you? That kind of thing happens all the time. That's why I don't use GitHub, for example.
My perspective on this is - To move fast, build product at a good speed, iterate and build new functionalities, to save time - we use 3rd party services after understanding their past record and kind of risk you go into if they stop - there is a silver lining to this.
I think Github is something you can be dependent on. Especially because they have been able to make it a profitable business. They charge for their service.
Whereas - branch.io is free for all. There is no clear business model as such. I would pay them a subscription fee and get a reliable service, rather than have a free unreliable service.
Suppose branch.io fixes their current problems, but next year goes totally bankrupt. How would that affect you? That kind of thing happens all the time. That's why I don't use GitHub, for example.