  We have produced persistent currents of ultracold fermionic atoms trapped in
a toroidal geometry with lifetimes greater than 10 seconds in the
strongly-interacting limit. These currents remain stable well into the BCS
limit at sufficiently low temperature. We drive a circulating BCS superfluid
into the normal phase and back by changing the interaction strength and find
that the probability for quantized superflow to reappear is remarkably
insensitive to the time spent in the normal phase and the minimum interaction
strength. After ruling out the Kibble-Zurek mechanism for our experimental
conditions, we argue that the reappearance of superflow is due to long-lived
normal currents and the Hess-Fairbank effect.
