If you read a little further on Mac went on to indicate that there are some apps that run in the background
Was there some indication that I didn't read a little further?
There are limitations to what an iOS app can do when backgrounded,
but those limitations are not the reason that StageMix doesn't hold connection.
Remoter is a 3rd party app that communicates with another computer,
just like StageMix, and unlike the core iOS apps that Mac mentioned.
It maintains the connection to the server when backgrounded.
It's up to Yamaha to make StageMix do the same.
Clearer now?