I am trying to export a session from my iPhone field recorder app to my desktop over wifi. I get a message on my desktop saying "connection broken”.

Yes, we have seen that problem occasionally. The thing is, that it has nothing to do with the software - but your wifi router. Sometimes it can help to restart the router. 
We do have another, simpler solution. You can import at session from the backup files in iTunes. 

Open iTunes.
Right-click on you iDevice and choose “Back Up”  

Open Hindenburg Journalist
From the menu choose: File / import from iDevice

Now you can browse and open any session from you iDevice

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