Hello lauw. It may be possible that the ZIP package is not available in your hosting environment or that the system resources needed to ZIP the created files exceeds what is available on your server. I would recommend contacting your hosting provider to see if any errors are occurring and to double check that the ZIP package is available and installed on your server.
Thanks for that additional info. It sounds like you may have to check your file or directory permissions and take a look to see if you have any security rules like a firewall that may be blocking access.