Okay, I'm still trying to hunt down a server to test with. I found something else to check while we wait. Make sure your switch is capable of autonegotiating speed on the interface connected to the LOM/s. Let me know what speeds the switch is capable of.
When the server has AC input power applied but is powered off, LOMs typically negotiate down the external link speed for reduced power consumption while still supporting Wake-on-LAN and/or shared network ports. These re-negotiations can create a momentary external link loss which may or may not interrupt any active remote management connectivity. If a connected switch is configured in a way to not allow for this dynamic speed negotiation, then remote management connectivity may not be available when the server is powered down.