UPDATE child
SET afield = parent.afield
FROM
atable child,
atable parent
WHERE (child.ParentID = parent.SelfID)
How about:
UPDATE child, parent
SET child.afield = parent.afield
WHERE (child.ParentID = parent.SelfID)
...if that doesn't work, try a subquery?
UPDATE child
SET afield = (SELECT parent.afield FROM parent WHERE parent.SelfID = child.ParentID)