I think this is a great question because not too long ago we struggled with the opposite question: How can electron-based molecules exist at all? (Funny that now I have to differentiate it from antiproton-based molecules...) The old model of atoms where electrons 'orbited' classically/astronomically interpret the electron as literally circling around the nucleus, and because a moving charge radiates energy electromagnetically it should shed it's orbital energy until it reaches the nucleus. This was a big conundrum way back before we settled on quantum mechanics, which solves this by recognizing that electrons 'orbit' is more like an acoustic standing wave and that there are a small number/quanta of available states that the electron can possibly exist in. Electron orbitals are not continuous or near-continuous, they are very much discrete, and there is some minimum activation energy required to shift between the various orbital states.
So I'd guess that the reason why the antiproton's orbit decays is because its orbital energy levels are "continuous enough" that its orbital energy can decay smoothly down to zero. Maybe this is related to the fact that the electron is relatively massless compared to the antiproton.
I think it's cool that we found a state of matter where the old model of atomic orbital motion that we interpreted as a paradox might be a physically accurate description in this circumstance.
This quora answer actually looks like a reasonable description of the issue past physicists faced: https://www.quora.com/Why-do-electrons-in-an-atom-keep-a-dis...
So I'd guess that the reason why the antiproton's orbit decays is because its orbital energy levels are "continuous enough" that its orbital energy can decay smoothly down to zero. Maybe this is related to the fact that the electron is relatively massless compared to the antiproton.
I think it's cool that we found a state of matter where the old model of atomic orbital motion that we interpreted as a paradox might be a physically accurate description in this circumstance.