Just found that my previous analysis was flawed. The problem is not related to the length of the patch cable. lii(4) comes up correctly if the eeePC is connected to the switch at the time when the eeePC is powered on. However, if the eeePC is not plugged in to the switch at powerup, then there seems to be no way to bring the link up later. Even a reboot does not help. Only cycling power appears to bring up the link to active state, and independent of the length of the patch cable.
Will take another look at the startup code in lii(4).