For the last few months, the iOS WordPress application had more and more problems connecting to my self-hosted blog. Deleting it and reinstalling the app helped only for a short time. As there was no change in the situation with the new Jetpack application, I had to figure out what was wrong.
The plugin configuration site of Jetpack showed me a 200: connection error and under Tools / Site Health I could reconnect my blog to Jetpack as often as I wanted, it did not change anything.
The only noticeable effect in WordPress was that the XML-RPC endpoint showed me an empty page. After disabling one plugin after another, I finally got the XML-RPC endpoint back to show me the desired output:
XML-RPC server accepts POST requests only.
The last deactivated plugin was Really Simple SSL. Deep down in its configuration you can deactivate XML-RPC, and that option will break your Jetpack connection. Make sure that you turn off Disable XML-RPC:
This little change was all it took to get the iOS app back into a working state. I hope this post can save you a lot of frustrating experiments to figure out what went wrong with your blog.