I back up the raw folder of encrypted data that is in my DropBox folder using a 'folder sync' program that runs automatically by a regular schedule. It copies any new files to the backup folder and deletes any files I deleted from BoxCryptor.
It does not matter if the BoxCryptor disk is 'mounted' or not when this happens. It takes less than 10 seconds using ChronoSync.
To recover files easily, in BoxCryptor preferences (paid version), I set up a second disk called 'Box-Daily-Backup' that points to the backup folder of encrypted data. With the same password as the original folder, I can mount the backup disk and then copy unencrypted files out of it, to either the Finder/Explorer, or back to my main working BoxCryptor disk.
My BoxCryptor folder is less than 1 GB, mostly text files, Excel etc., so I make multiple backups using multiple automated folder syncs:
All of these are set up as BoxCryptor disks in my BoxCryptor preferences, although only the working folder is set to auto mount on log in.
[I am presenting this as an alternative to using Carbon Copy Cloner to backup the mounted, unencrypted volume. I use SuperDuper! for backup clones of my main boot drive, but even SD does not 'see' a BoxCryptor volume as a disk (although it does see mounted disk images as disks). I prefer my method because the backup data is encrypted, too]