Thank you for your clarification.
With these, I can say that Cron and backup commands (rsync) are not responsible for your problems.
It is also clear that you lose the connection to the remote share:
The interesting thing here is that if I then go to "File Share menu/Backup". And then try to click the new remote source, nothing happens (I can not choose it as I did before)
If you can not browse the tree is that the connection is lost.
The question is why?
Since you're apparently the only one with this problem, I think either your network or your PC are the cause of that.
If you made a backup NAS -> PC, have you the same problem ?
Finally what is the OS of the PC?
To validate that the NAS is not involved, it is necessary to verify if the relevant mount points of remote share are still present.
In putty, run the "mount" command. In the output, you must have two lines that start with:
"//addrIp/sharename,
addrIp which is the address of the PC.