gistfile1.m

// Notification name as a constant, keep things clean. You'll see why this is needed soon.
static NSString* const MyStopNotificationName = @"MyStopNotificationName";

// Somewhere in your code you've got a button...
[self.someButton addTarget:self action:@selector(startConnection) forControlEvents:UIControlEventTouchUpInside];

// Somewhere else you have this method implemented
- (void)startConnection
{
    self.someButton.enabled = NO;
    [[NSNotificationCenter defaultCenter] addObserver:self selector:@selector(stopConnection) name:MyStopNotificationName object:nil];
    // It does the thing that is required to start your connection. Forget about setting connectionStarted, you don't need it.
}

- (void)stopConnection
{
    // This is called when that notification is posted, and only then.
    self.someButton.enabled = YES;
}

// Whenever you would have set the connectionStopped boolean, do this instead:
[[NSNotificationCenter defaultCenter] postNotificationName:MyStopNotificationName object:nil];

// Profit!