We show that in the severe slowing-down temperature regime the relaxation of antiferromagnetic rings and similar magnetic nanoclusters is governed by the quasicontinuum portion of their quadrupolar fluctuation spectrum and not by the lowest excitation lines. This is at the heart of the intriguing near-universal power-law temperature dependence of the electronic correlation frequency omega(c) with an exponent close to 4. The onset of this behavior is defined by an energy scale which is fixed by the lowest spin gap Delta(0). This explains why the experimental curves of omega(c) for different cluster sizes and spins nearly coincide when T is rescaled by Delta(0).