You need to ask the OS for the application to work, it has nothing to do with Dropbox ... When you start the download, do the following:
UIBackgroundTaskIdentifier bgTask = [[UIApplication sharedApplication] beginBackgroundTaskWithExpirationHandler:^{ [[UIApplication sharedApplication] endBackgroundTask:bgTask]; }];
... and save bgTask somewhere. Then, when your download completes or fails, do the following:
[[UIApplication sharedApplication] endBackgroundTask:bgTask];
This will mean that the OS will support your application, because the background task is running there ...
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