Wake-on-Lan working only intermittently

Hi. I'm trying to use Wake-On-Lan. I turned it on for the onboard
NIC in the system BIOS of the machine in question. When I send the
WOL magic packet it works...sometimes. Other times, the target
machine doesn't wake up. The system gets in some state in which it
will not respond to any WOL packets. If I boot it up manually to the
production OS and shut it down, it sometimes gets back into a working
state for awhile.

Here's what little troubleshooting I've done so far:
- WOL works sometimes, so it's not that I haven't enabled it in BIOS
on the target machine.
- I've used a couple of different WOL-sending tools with the same
results
- I verified the magic packet is getting sent and is correct
(Broadcast UDP packet containing FF FF FF FF FF FF followed by the
target MAC address repeated a bunch of times) by using a network
sniffer on the sending machine. It is getting sent correctly even in
the case when the target machine is not waking up.
- I verified the magic packet is getting sent and is correct by using
a network sniffer on another machine that is "adjacent" to the target
machine (it connected to the same physical switch, so nothing in the
network is blocking the packet between the sender and the switch right
before the target machine). It is getting received even in the case
when the target machine is not waking up.

Any ideas what the problem might be? Are motherboards or NICs
typically flaky with regard to WOL? Might the switch not be sending
the magic packet to the port the target machine is connected on for
some reason ? (It somehow detects the target machine is off and so
thinks there is no point in forwarding the packet?)

Thanks,
Dave