We once had an Ericsson MSC that only replied to _uneven_ ICMP packets due to some bug.
Made it look like there was 50% packet loss on an otherwise perfectly good Cat 5 cable...
(edit: ICMP instead of IP)
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We've had a 3rd party router configured to balance traffic based on even/odd last octet. Add faulty hardware and DHCP to the mix, and here you have really hard to debug problem.
Checksum issue?
IIRC, there was nothing on the logs and they eventually shipped a fix. I was there when it happened and was called over to have a look.