The recently discovered giant magnetic anisotropy of single magnetic Co atoms raises the hope of magnetic storage in small clusters. We present a joint experimental and theoretical study of the magnetic anisotropy and the spin dynamics of Fe and Co atoms, dimers, and trimers on Pt(111). Giant anisotropies of individual atoms and clusters as well as lifetimes of the excited states were determined with inelastic scanning tunneling spectroscopy. The short lifetimes due to hybridization-induced electron-electron scattering oppose the magnetic stability provided by the magnetic anisotropies.