I got an email from a Seagate tech who read this forum (very good news) and sent me a clue that some process must be trying to transfer to the drive. After some trial and error, I have determined that Zone Alarm firewall is the culprit. Now I have to figure out if there is a way to have both co-exist without this problem. Any ideas??
update: I found how to tell zonealarm to leave the maxtor alone...
in anti-virus/ anti-spyware advanced options (when the maxtor is connected), select scan targets, drop down local hard drives, and deselect the maxtor.
It stops flashing, and the safely remove option works.