Yes, it seems your onboard ethernet is not fully compatible with ZS.
I already had this type of problem with another “linux” firewalls.
The easier solution is to add another network card, old hardware is better for Linux 🙂
Another solution, you could try to set the ethernet speed and media sense but it doesn’t work every time:
ethtool -s ETH01 speed 100 duplex full autoneg off
Take speed and media infos from the network page of ZS.
If it works you should put this command in the startup script.