A paradox is an internal inconsistency. Noone claims that quantum mechanics is the fundamental theory of everything. Like the convergence of a taylor series, there is a range of energies within which it produces correct calculations, and if you go outside that the result is undefined.
Strictly speaking that is a QFT problem, or really a standard model problem, moreso than a quantum mechanics problem. In order for it to be a quantum mechanics problem it would have to happen everywhere in quantum mechanics, and the single electron Schrodinger equation hydrogen atom definitely has no (theoretical) problem.
