One major drawback of Rutherford's model was the comparison of electrons with the planets in the solar system.
Thus, when an electron moved around the nucleus continually, it should radiate energy, i.e. lose energy. As a result it should be gradually pulled towards the nucleus and end up colliding with it. This should result in the total collapse of the atom.
However, we know that the atom is structurally stable. Thus, Rutherford's model could not explain this stability.