We report a systematic molecular dynamics study of the isochoric equilibration of hard-sphere fluids in their metastable regime close to the glass transition. The thermalization process starts with the system prepared in a nonequilibrium state with the desired final volume fraction ϕ for which we can obtain a well-defined nonequilibrium static structure factor S(0)(k;ϕ). The evolution of the α-relaxation time τ(α)(k) and long-time self-diffusion coefficient D(L) as a function of the evolution time t(w) is then monitored for an array of volume fractions. For a given waiting time the plot of τ(α)(k;ϕ,t(w)) as a function of ϕ exhibits two regimes corresponding to samples that have fully equilibrated within this waiting time [ϕ≤ϕ(c)(t(w))] and to samples for which equilibration is not yet complete [ϕ≥ϕ(c)(t(w))]. The crossover volume fraction ϕ(c)(t(w)) increases with t(w) but seems to saturate to a value ϕ(a)≡ϕ(c)(t(w)→∞)≈0.582. We also find that the waiting time t(w)(eq)(ϕ) required to equilibrate a system grows faster than the corresponding equilibrium relaxation time, t(w)(eq)(ϕ)≈0.27[τ(α)(eq)(k;ϕ)](1.43), and that both characteristic times increase strongly as ϕ approaches ϕ(a), thus suggesting that the measurement of equilibrium properties at and above ϕ(a) is experimentally impossible.