Looks most likely like a problem with the ethernet card, especially with the way the hardware address zeroes out.
If you wanted to watch it for a while, I'd use cron to regularly log
(every minute) the output of '/sbin/ifconfig eth0 | head -1'
You could also use the watch (1) command, which is in sys-apps/procps.
$ watch "/sbin/ifconfig eth0 | head -1"
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