So I understood...
You did not select the option "SSH Access with rsa key" and when you use ssh-copy-id (which is not included in our firmware) it creates some files which allows to use this mode at the same time with the mode "SSH Access by pwd". So when you reboot the nas, the firmware removes these files.
We want to keep the following behaviour with our firmware : do not to allow both modes at the same time... It is our choice because usually the key mode is often used to get a WAN remote access and then you must open the ssh port. This port is systematically sniffed by some malicious bots and you can got some database on the net according with the researched machine profile. I post here an example with the apache server:
http://www.base64online.com/hc.php?q=fvdw-sl%20NAS%20Management. So with these two hosts (old recording,I know it is a machine using our firmware and I can also try to connect to the ssh server !!! As the default login is known (and I found a site which lists it!) I will get a root access if the user does not have yet changed the password !
And think at each time you upgrade the firmware the custom password of the root account is also reset...
So in your case, do not use ssh-copy-id and you just have to change the login mode and paste your public key. (Please to read the help page)