It is all about nuclear stability. Stable nuclides do not naturally undergo nuclear decay. Unstable nuclides naturally decay in accordance with their respective half-life. A nuclide is a specific atom and neutron combination. Isotopes are nuclides with the same number of protons. When you say that an element can have, for example, 3 isotopes I think what you really mean is that there are 3 stable isotopes. An element can have radioisotopes (radioactive isotopes). Tin, for example, has the highest number of stable isotopes (10). It has a bunch of radioisotopes too which all decay with their own unique half-life. There are minerals on Earth containing unstable nuclides. All isotopes of uranium, for example, are unstable. These isotopes simply haven't existed long enough to decay. Technetium, element 43, has no stable isotopes and essentially doesn't exist naturally at all on Earth. In reality even "stable" isotopes decay, but at far too slow a rate to be noticeable. Bismuth-209 was thought to be a stable isotope until 2003 when it was demonstrated that it has a half-life a billion times longer than the age of the universe. Nuclear stability can be estimated by proton/neutron ratio as well as total proton and neutron count. The nuclear physics that determines stability is mostly beyond my understanding. Ultimately the stability of an isotope has to be measured experimentally. This interactive chart shows the stability of nuclides: