Why would the NIC only break once after the ME is neutralized? The system is started from a fully powered-off state after the ME firmware is updated. Maybe the NIC has some sort of non-volatile state that gets updated when the ME fails to initialize, and then the NIC starts working again. That's the most complex explanation so I thought it unlikely, but I'm happy to hear more from someone who has actually neutralized their ME.
After a reboot, the NIC starts without the ME ever taking control of it, so it works.
It's not strictly clear to me, but reading through what they're doing, the ME isn't re-engaged or its unclear how it recovers itself.
Unless the ME is operating with a recovery binary somewhere that isn't covered by Nicola's neutralizer and the subsequent flashing, I don't think it comes back in to normal operation.
"With ME neutralized, the MEI interface disappears from the PCI bus, and the integrated NIC ceases to work, but will resume to work after a reboot."