I mean, the GUI object with its reference to the network request should never be detached like that. The network request handle should be moved to something else that takes care of it, if the GUI object can't, and it should not be calling a callback tied in a strong way to the GUI object's existence. Granted, I wasn't there when you had this, and I'm not saying there's an easy solution. What I am basically saying is there should be a chain of ownership to some local variable on the stack somewhere, instead of a detached GUI view. I'd view the resource leak you describe as hacky, and a class of design decision that has caused me a lot of pain in gui software. Well, maybe I had to be there.
Yes, you can move your references around to find a suitable place, but how does that solve the problem of lifetime control? How do you guarantee a network resource is alive for as long as you need it under GC, and under ARC?
By holding a reference to it that is grounded to a GC root i.e. an an ownership chain to a local variable that will dispose of it. Also which can be used to interrupt the background task. So the network connection, callback, etc., are not in a detached cycle.
With the design you're describing -- without the ability to interrupt the background task -- I would bet you tend to get race conditions of one kind or another.