The easiest way to solve this problem is to run a transaction with the “Enable Debug” checkbox checked from the settings menu. The following URL should explain more on this:
How to Test the WordPress eStore to Make Sure Everything is Working Properly
We need to see what the plugin is doing after the payment. So do the above mentioned step and provide me the content of the “ipn_handle_debeg.log” file and you will see how quickly this gets resolved.