How about you change your strategy and mount and unmount the shares as needed for your backup. You could also add some code to check that the backup server is online by pinging it before auto mounting and either waiting for it to come on line or fail the backup. In pseudo code:
Ping remote server and see if it is on line.
If not, wait for it to come on line, or fail the backup script.
rc.unassigned mount <backup remote share>.
Perform the backup...
rc.unassigned umount <backup remote share>.
I wouldn't have dockers running depending on the remote mount to be available if it is turned off. Coordinate the use of the mount points with when the backup server is on line.