SteveITS actually sort of hit upon the issue in his reply, which is how mapping is happening.
If I login as User 1 and I map the network drive, user 2 is unable to see the drive. That's because the mapping is happening in User space.
3CX on windows runs using the services, which are likely using "Local System". Local System cannot see the drive maps of a user.
You have several ways to deal with this. These first 3 are not so great ideas, but still do-able.
1) The above mentioned xcopy/robocopy options
2) mapping the drive in the context of the user running the 3CX services (open up the services control panel applet, see who the "log on as" is set to. You can setup a scheduled task to run as local system that calls a batch file with net use to map a drive in that context
3) change the service to run as the user you are logging in with.
However, the correct way to solve this is built into 3CX - simply backup to SMB instead of local disk.
See, your network mapped drive is connecting to a SMB server already. Simply load that information into 3CX and away you go.
4) use the backup to SMB option