I'm currently using the latest Webextensions version of uBO beta. My problem might also occur on the legacy version.
When downloading or creating a backup file Fx places the file in Windows Temp folder. It is something like xxxxxxxxx.fileextension.part. This is to allow the file to continue to be downloaded if you exit Fx and then get back into it. After a successful download the .part is removed and the file should then be called xxxxxxx.fileExtension.
In the case of uBO after clicking on the Backup button the backup appears in the Temp folder as +JZgrPdd.txt.part. The first part of the name will always be different each time you do a backup.
There are two issues I believe:
The file should be renamed with a file extension of .txt. From what I read on your Blog the filename should be a lot longer.
The backup file doesn't seem to be in any other folder. At least I can't find it.