Strange. Try this: In Windows Explorer go to the folder
C:\Users--username--\AppData\Roaming\Blueberry Software\FBXGameRecorder
And delete CommonSettings.xml
And try again. You'll be asked to create an account again - just use the same google/facebook/email account you used before.
If it still doesn't start: go to the Windows Start button, search for "FBX", open the "FBX Game Recorder" folder that appears in the search results, select "Send a Problem Report"