Issues with document syncing between iOS and host computer
Did you sync with a computer that you don't usually use? If you lost the app, you lost it's Documents directory, and your recording is gone.

Here's what is supposed to happen;

You're supposed to open iTunes and browse to your device. In the list of apps with the iOS Home Screen style view, there is a section at the bottom to select an Application, and manage it's Documents storage folder.

You do not need to sync in order to view up-to-date information in this screen. You are immediately able to save the data out of the app into a location on your computer.

Unfortunately, if you've sync'ed your phone and lost the app you've also lost the data from within it. There is little likelihood for data recovery on a Flash Disk device.