I currently own a Z570 and I'm facing some issues with my touchpad.
When I attempted to disable it by using Fn+F6 and then re-enabled it using the same way, it did not seem to work. I needed to restart the laptop to get it worked again.
Is there anyway to get this working without the need of restarting the laptop?
There is possibilty that your touchpad driver and Energy Management driver (which enable hotkeys too) may not work properly. A community user got the touchpad work again for good after re-installed the mentioned drivers.
Go to Start > Control Panel > Programs and Features.
Uninstall the TouchPad driver and Energy Management driver.
Download and install the updated TouchPad driver and Energy Management driver from the Lenovo Support site.
Note: Remember to verify whether the issue is fixed or not after installing both the drivers. Optionally, you may also want to consider an update of the BIOS for your system as this is recomended to ensure the system runs at at optimal performance. If you're not familiar with BIOS update, please do not do it but get service engineers to help.