To permanently allow a user to install updates via update manager in Linux Mint, a policy needs to be added to PolicyKit (polkit):

sudo vi /etc/polkit-1/rules.d/99-mintupdate.rules

replace 'username' with the actual user

javascriptpolkit.addRule(function(action, subject) {
    if ((action.id == "com.linuxmint.updates.install" ||
         action.id == "org.freedesktop.packagekit.package-install" ||
         action.id == "org.freedesktop.packagekit.package-update") &&
        subject.user == "username") {
        return polkit.Result.YES;
    }
});

then either reboot or restart the polkit service:

sudo systemctl restart polkit