Enabling this feature takes a couple steps, but once it is done, you should be able to download the recordings for offline viewing.
First, go to Administration > Compliance and Control > Recordings and Notice and check the box to Allow for distribution of local copies of recordings to end users

Next browse to the desired recording(s) and go to the Edit Information page. This is done through the Edit Information if the recording is in the Content library, or by selecting the recording name and then the Edit link in the Recording Information header (not the Edit Recording button). Check the box for Allow Users to download copy to local device

Now in Connect Desktop, you will see the Fetch button for recordings that are set up to allow local downloads.
