I looked this up on Wiki. Apparently, the reason for the stability of this excited state of Ta 180 is its high spin (9 units) compared to the lower lying states to which it could decay. This implies that any transition to a lower state would require the exporting of several units of angular momentum at once. A photon, which would be emitted in gamma ray decay process, has a spin of 1 unit. The other decay modes would involve emission or capture of an electron, which is a spin 1/2 particle. Consequently it can only decay by a process involving simultaneous emission or capture of multiple QM entities - intrinsically a very low probability event. But if you ask me why Ta 180m has to have a spin of 9, I have no idea. We would need a nuclear physicist to explain that to us.
The half life being what it is, and many times longer than the age of the Universe. One also wonders about the possibility of the decay of the proton in relation to the age of the Universe.
It seems to me a half life as long as that is just a way of saying it is stable. I suppose what is unusual is for a quantum state other than the ground state to be completely stable. To me, the strange thing is the very high spin of this state, which is apparently the reason for its stability. I looked a bit further into the issue and it seems there are several cases in nuclear physics in which an excited state is more stable than the ground state. An example is In 116, which has an excited state with a half-life of 54mins, whereas the ground state (which decays to Sn 116, by β-decay) has a half-life of only 14secs! Again, the reasons for the stability are to do with angular momentum and the associated selection rules for nuclear transition processes. (By the way, I did not even know there were such things as excited nuclear states until a year ago, when my father underwent a hospital scan procedure that relied on injecting Tc 99m, which is metastable, with half life of 6 hrs, I think. We live and learn. I pulled his leg a bit about glowing in the dark. )
I don't how there could be, since neither decay has ever been observed. All we have, experimentally, is a lower limit to stability based on this fact. But I see, from looking it up, the Standard Model predicts the proton to be indefinitely stable, in agreement with observation to date. There are, it seems some Grand Unified Theory scenarios that predict proton decay but, so far, nowt, rien, sifr, nada.
Actually, it is string theory that predicts proton decay, although string theory also figures prominently in some versions of a GUT. When a string theorist is presented with experimental data that indicates the proton doesn't decay within the current age of the universe, they only shrug and say that nevertheless, proton decay is predicted. I suppose there is a sort of logic in that. The tantalum finding is interesting, nonetheless. If string theory predicts a very long decay rate for the proton, you might think they would have a decay prediction on the same order for tantalum or Zirconium 69 (half-life = 2 x 10^19 years) as well, but they don't. Therein lies the problem with string theory; long on any kind of prediction that can't actually be tested, and just as long on "predicting" things that are already a certainty, or basically any other result you might want in between.
The prediction (which agrees with observation) about Ta 180m derives from ordinary QM. These selection rules are something I am familiar with (in the context of excitation of electrons and molecular vibration and rotation) from atomic and molecular spectroscopy. So I don't imagine a GUT would have anything very different to say about them.
