Some theories predict that protons decay, but the half life is like 1E31 or 1E35 years (compare to the Xe124 that has a half life of only 1E24 years). All experiments so far to measure the proton decay have failed, anyway. https://en.wikipedia.org/wiki/Proton_decay

I don't remember anything specific about deuterium, and the method that Xe124 uses is not available, and I can't imagine a razonable alternative method, so my guess is that deuterium is as stable as protons.