Put FEBE in debug mode (FEBE Options > Advanced > Miscellaneous > Advanced Preferences). This should open the error console. If it doesn't, click the Toggle browser (error) console button.
Make sure the "JS" button in the console is on (click to turn on/off - dark is on, light is off). Run a backup and examine the console for any FEBE related error messages (type febe in the "Search:" box). Copy/paste them here.
You should also try running "Clear FEBE preferences", "Verify extension directory" and "Check AddonManager functionality" in FEBE Options > Advanced > Tools. FEBE will alert you if it finds any problems.
When done, you can hide the error console by unchecking the FEBE debug mode box in FEBE Options > Advanced > Miscellaneous > Advanced Preferences. Or (if you have the browser console open) click the "X" button in the console's upper-right corner.