Question

Why can't astronomers measure the parallax of a star that is a million light years away?

Answer 1

One of the methods used widely to calculate the distance of nearby or closer objects in astronomy is Parallax. The distance of the stars are usually expressed in light years but the unit of distance is parsec or parallax second.  

                                        1 Parsec = 3.26 light years

Astronomers are not able to measure the parallax of a star that is a million light years away because the star is too far and the distance with which the start appears to move is too less to be calculated accurately.