Rutherford's atomic model could not explain stability of atom.
Rutherford's model described the atom as a tiny, dense, positively charged core called a nucleus, in which nearly all the mass is concentrated, around which the light, negative constituents, called electrons, circulate at some distance, much like planets revolving around the Sun. According to the model electron’s speed will keep reducing as the electron keeps giving off energy by emitting radiation and the radius of its rotation will keep decreasing and it will soon crash into the nucleus which does not happen.
Hence, we can conclude that Rutherford's atomic model could not explain the stability of the atom as a whole.