RTL810xE PCI Express Fast Ethernet controller Failed

You could try increasing the grub timeout to 10 seconds from 5. It was reported on the Arch forum as possible that it needs time to power up or it doesn’t load the module.

This is done in /etc/default/grub

Then update grub with sudo grub-mkconfig -o /boot/grub/grub.cfg

This is something you can check as it should use the r8169 module i think.