Just an FYI for people reading this thread with similar problems.
After installing the OS in our environment, the host initially comes up with a DHCP-assigned address, and a Powershell script waits for this to happen, then changes the IP address and other information to the correct static IP address.
In ESX 6.0 this causes a restart of the management network.
In ESX 6.5, the behaviour is slightly different, and the management network didn't seem to completely restart. The problem goes away when the management network is manually restarted from the console.
Next step is to look at how to achieve this through PowerCLI, although since this only happens once at build time, we may just use PowerCLI to reboot the server after these changes are completed.