  Despite the formal analogy with the Higgs particle, the amplitude
fluctuations of the order parameter in weakly-coupled superconductors do not
identify a real mode with a Lorentz-invariant dynamics. Indeed, its resonance
occurs at $2\Delta_0$, which coincides with the threshold $2E_{gap}$ for
quasiparticle excitations, that spoil any relativistic dynamics. Here we
investigate the fate of the Higgs mode in the unconventional case where
$2E_{gap}$ becomes larger than $2\Delta_0$, as due to strong coupling or strong
disorder. We show that also in this situation the amplitude fluctuations never
identify a real mode at $2\Delta_0$, since such "bosonic" limit is always
reached via a strong mixing with the phase fluctuations, which dominate the
low-energy part of the spectrum. Our results have direct implications for the
interpretation of the sub-gap optical absorption in disordered superconductors.
