By marrying his daughters to sons of the reigning emperor and then engineering timely abdications, a Fujiwara contrived always to be father-in-law, uncle, or grandfather behind the throne.
The Fujiwaras always stayed in power  because they carefully constructed familial marriages and arrangements as to forever have male family at the throne.
Fujiwaras failed to stay at the forefront of the empire when an unrelated male married his way to the top.