What would preclude Herod from dying a year after Jesus was born?
Herod ordered the death of boys two years old and younger, based on the information he had obtained from the Magi, implying that the Magi told him that the star began to appear two years before.
The Herod who met with the Magi was the father of Archelaus (Matt.2.22), who reigned from 4 B.C. to A.D. 6.
What would preclude Herod from dying a year after Jesus was born?
You are thinking in the wrong direction of time.
4 B.C. is before 3 B.C.
4 BC is a year before 3 BC.