You need to make a multithreaded application. Then you can have a background thread polling the server (or better, making asynchronous requests on it.
Have a look at the NSOperation and NSOperationQueue classes. You'll make each background task be represented by an instance of an NSOperation class. This class takes care of starting the operations, making sure that they are run in the appropriate order, and accounting for any priorities that you set.
The most common way to use NSOperation is to write a custom subclass and override the method, main. The main method gets called to perform the operation when the NSOperationQueue schedules it to run.
If you don't want the overhead of subclassing, take a look at the NSInvocationOperation class. This is a concrete subclass of NSOperation that makes it easy to attach an operation to an existing method. NSInvocationOperation objects can be added to an NSOperationQueue (just like NSOperations), so that you get multi-threading without having to subclass.