Note that the behavior is different depending on which version of the app you're using.
For the iPhone/iPod version of the app, you will lose your dictation if you exit the app. In order to keep a copy, you will need to send it to yourself by email or SMS before you leave the app. You can also copy the dictation using the Copy feature and once you leave the app, paste the content of the clipboard into any other application that will allow you to save the text as a note for future viewing.
The iPad version of the app does have a Notes section that allows you to save your notes as draft after you leave the app. If you choose to email your dictation, it will no longer appear in the Notes section of the app.