You need to disable compilation option before taking any backup if enabled.
and then after take backup so it can work when you restore.
This fetal error has been there since version 1.6 and is related with file/folder permissions.
Please check server logs and it will lead you to the exact path where it is trying to make backup files and resulted in failure.
If you are using a hosted service then you can contact your vendor about it letting them know the details.
On a self maintained server simply using standard system commands can fix this problem.
Sometimes changing permission of the index.php to 644 also works depending on the operating system you are using.