  We investigate the stability of persistent currents in superfluid fermionic
gases confined to a ring geometry. Our studies, conducted at zero temperature
using time-dependent density functional theory, cover interaction regimes from
strong (unitary Fermi gas) to weak (Bardeen-Cooper-Schrieffer regime)
couplings. Stability is tested with respect to the presence of an external
defect within the ring. The dissipation mechanism related to vortex generation
is present in all interaction regimes. Interestingly, while the corresponding
critical winding number is found to be independent of the regime, the flow
energy dissipation and its origin strongly depend on it. Vortex emission is
accompanied by Cooper pair breaking, which occurs even beyond the vortex core
in the weakly interacting regime. The pair-breaking mechanism prevents the
imprinting of a persistent current with a winding number above a threshold,
which decreases as we approach the BCS regime. Our study reveals the existence
of two types of critical winding numbers above which the currents cease to be
persistent in Fermi superfluids: one related to the proliferation of quantum
vortices and the other with the onset of the pair-breaking mechanism.
