I would assume that it is a permissions problem. I am not familiar with Norton Scheduler, but the Windows task scheduler allows you to set the user to run the batch as. If Norton's doesn't have that option then there are other ways to get it done inthe batch file itself.
Replace the copy with these lines to see if it works ( the 'net use' continues all the way to the username it wraps in this window):
net use z: \\server1\backup password /USER:domainname\username
copy backup.zip z:netuse z: /delete
You may replace the 'z:' with any drive letter that would be available when the batch file runs. Put the password of the user who has access to the share where it says password, and replace domainname\username with the username of the user whose password you used. For example if the user 'johndoe' belonged to the domain 'FOO' and his password was 'xyz' that section of the command would look like this:
net use z: \\server1\backup xyz /USER:FOO\johndoe
For more help typeon the net use command type 'net use ?' at a command prompt.