[evanb]

The "at some point" doesn't have to do with time. It has to do with the rest of the wavefunction of the universe. If the atom becomes entangled with everything else (in fact, a single quantum-mechanical spin suffices) the two branches become orthogonal and the interference terms from 'merging' vanish. We say the wavefunction 'decohered' when it becomes too complicated to see how to reverse this effect---as more and more particles get involved it becomes hopeless.