Detect the reachability in background

Live you cannot change if the network connection changed, the very best you can do to make it work is to use Background Fetch mode from Capabilities. Firstable you need to check the checkbox for background mode:

Then you need to ask for time interval as often as you can the sooner the better so i suggest application:didFinishLaunchingWithOptions: and you need to put this line:

- (BOOL)application:(UIApplication *)application didFinishLaunchingWithOptions:(NSDictionary *)launchOptions {    [application setMinimumBackgroundFetchInterval:UIApplicationBackgroundFetchIntervalMinimum];    return YES;}

The UIApplicationBackgroundFetchIntervalMinimum it's as often as possible, but it's not exact number of seconds between fetches from the docs:

The smallest fetch interval supported by the system.

And then when background fetch will fire you can check in AppDelegate with method:

-(void)application:(UIApplication *)application performFetchWithCompletionHandler:(void (^)(UIBackgroundFetchResult))completionHandler{    Reachability *reachability = [Reachability reachabilityForInternetConnection];    [reachability startNotifier];    NetworkStatus status = [reachability currentReachabilityStatus];    switch (status) {        case NotReachable: {            NSLog(@"no internet connection");            break;        }        case ReachableViaWiFi: {            NSLog(@"wifi");            break;        }        case ReachableViaWWAN: {            NSLog(@"cellurar");            break;        }    }    completionHandler(YES);}

All of this will work in iOS 7.0 or higher.

I don't believe there is a way to receive reachability notifications while you're in the background. The correct way to handle this would be to check for reachability in AppDelegate's - (void)applicationWillEnterForeground:(UIApplication *)application.

The only background event that background apps react to is receipt of push notifications, and that is because the OS wakes them up to do so, and then only when the user requests it.