How to remove the loading wheel from iPad home screen?
Possibility 1: Bug in a third-party app

Third-party developers have the ability to turn this icon on and off in their applications. This is a problem when the app does not disable the icon appropriately when it is finished with network operations. 

The spinning wheel is set based on the networkActivityIndicatorVisible property and is set like so:

[[UIApplication sharedApplication] setNetworkActivityIndicatorVisible:YES];

Restarting the device fixes this until the offending app enables the icon and, once again, does not disable it. Apple apps will handle the icon properly, but iOS leaves it up to the third-party developers to handle it on their own. Sloppy developers can definitely cause the issue you are seeing.

The explanation from Apple's developer page on this topic:


  Specify YES if the app should show network activity and NO if it
  should not. The default value is NO. A spinning indicator in the
  status bar shows network activity. The app may explicitly hide or show
  this indicator.


Because this is explicit, bugs in code may cause this to remain visible long after a network operation finishes. My suggestion to you is to track down the offending app and submit a bug report to the developers.



Possibility 2: Actual networking is happening in the background

The accepted answer from this Apple.SE question suggests that it may be actual network activity causing the spinning wheel to remain visible. 


  
  The network you've connected to needs some more configuration, and it's taking some time to get the configuration information set
  properly from the router (or, more likely, DNS server)
  Your phone is polling for a lot of data to transfer - maybe there are a lot of apps to update, or you have a lot of email to sync, or
  you have a lot of cloud data to download
  Your phone is trying to hit an important server, and is having trouble connecting to it (say, it's trying to poll apple servers to
  check for software updates and the servers in questions are down). The
  spinner is going to stay up for a while, until your phone gives up or
  gets an actual connection.
  


This is certainly possible. It may not be a bug in anyone's code and reflect actual networking that your phone is doing in the background.