Sometimes, electronics do fail that way, known as 'warm-up faults',
usually caused by a bad joint, either internal or external to the chip.
What might be happening is that when the LAN chip is doing some
work, it heats up to a failure temperature. It probably won't work
again until rebooted, even if it cools below the failure temperature.
Improving the cooling inside the PC case might be enough to fix it.
HTH,
--
Rob