I have the same hardware and the same problem. In order to support WOL, the Asus H87I-Plus requires an option set in the BIOS (Onboard>APM>Power on by PCIE). When I have this enabled, I can indeed start the machine using the wol magic packet, but there is an undesired side-effect: when I shutdown the machine, it stays shut off for about 5 sec and then turns back on all by itself. If I disable the option in the BIOS, this does not happen... but I am unable to use wol.
Can you post the output of ethtool eth0 for me? Here is the output of my command:
% sudo ethtool eno1
Settings fo