The "Event ID 2087: DNS lookup failure caused replication to fail" link provides suggestions on the troubleshooting approach for this problem.
This event was cleared on my PDC by listing the BDC as the DNS on both NICs (it is a multi-homed PDC and originally had its own IP addresses listed as its DNS). Doing this also cleared event 1053 and 1054. In this case, at boot up I believe the DNS services on my PDC did not start fast enough to allow it to find the other domain controllers.
See the link to "Troubleshooting Active Directory Replication Problems" for details on solving this problem.
This event can be ignored if it occurred when Windows was started in Active Directory Restore mode or some other form of Safe Mode. Otherwise, investigate further.