We have measured the lifetime of spin imbalances in the quasiparticle population of a superconductor (\(\tau_s\)) in the frequency domain. A time-dependent spin imbalance is created by injecting spin-polarised electrons at finite excitation frequencies into a thin-film mesoscopic superconductor (Al) in an in-plane magnetic field (in the Pauli limit). The time-averaged value of the spin imbalance signal as a function of excitation frequency, \(f_{RF}\) shows a cut-off at \(f_{RF} \approx 1/(2\pi\tau_s)\). The spin imbalance lifetime is relatively constant in the accessible ranges of temperatures, with perhaps a slight increase with increasing magnetic field. Taking into account sample thickness effects, \(\tau_s\) is consistent with previous measurements and of the order of the electron-electron scattering time \(\tau_{ee}\). Our data are qualitatively well-described by a theoretical model taking into account all quasiparticle tunnelling processes from a normal metal into a superconductor.