Hello.
I think this behavior is to lead back to the new ios Version 13…
As I updated my iPhone to iOS 13, i had exactely same behaviour.
But my wife was still on iOS 12.x… and it worked for her. We are usuing 3 of balena Sound RPi 0W. The behavior was exactely same on all 3 of them. Since my wife updated to iOS 13.1 she has the same problem. Balena Sound become unusable 
But the general bluetooth connection works with all other bluetooth receiver, like our cars, Audioengine B1, Technisat Internet Radio, Panasonic and Beats headphones, etc. But it will not work with balena Sound with same behavior on all 3 RPi’s, while another Android Phone can still use it.
I think, apple has changed something in the bluetooth-connection in iOS 13.x. This is what you should have a look at it.
Please have also a look at: Music will skip and or pause using Balena Sound