I just installed the addon and FEBE still works for me.
Please post the FEBE related errors in the error console (Tools > Error Console) using the extension for error checking.
Try this: Open and clear the Error console. Leave it open and perform a backup. After a few seconds (when the progress meter starts moving again) examine the error console for any FEBE related error messages (type febe in the "Search:" box and make sure only the "Errors" tab is selected ... not "All", "Warnings", or "Messages"). Copy/paste them here.
Also try running "Clear FEBE preferences", "Verify extension directory" and "Check AddonManager functionality" in Tools > FEBE > FEBE Options >Advanced.