We investigate the aging properties of phase-separation kinetics following quenches from T=∞ to a finite temperature below T_{c} of the paradigmatic two-dimensional conserved Ising model with power-law decaying long-range interactions ∼r^{-(2+σ)}. Physical aging with a power-law decay of the two-time autocorrelation function C(t,t_{w})∼(t/t_{w})^{-λ/z} is observed, displaying a complex dependence of the autocorrelation exponent λ on σ. A value of λ=3.500(26) for the …