Rutherford's model could not explain the stability of the atom. This is because according to Rutherford's model, an atom consists of a small heavy positively charged nucleus in the centre and the electrons were revolving around it. These revolving electrons would lose energy as they are the charged particles and due to acceleration charged particles would radiate energy.
Thus, the orbit of the revolving electron will keep on becoming smaller and smaller, following a spiral path and ultimately the electron should fall into the nucleus. In other words, the atom should collapse.