The onset temperature, Tirr, for magnetic irreversibility in high-temperature superconductors has been investigated as a function of frequency (0.2 Hz≤f≤65 000 Hz) and DC magnetic field (0<H<4000 Oe). In Y-Ba-Cu-O crystals Tirr is essentially independent of the frequency, while in Bi-Sr-Ca-Cu-O and Tl-Ba-Ca-Cu-O crystals Tirr exhibits a strong frequency dependence. For all three systems Tirr(H) converges to a finite temperatureas the frequency approaches zero. Analysis of the experimental data shows that conventional theories of thermally-activated vortex motion cannot explain the measured frequency dependence of Tirr. Rather, the data indicate that Tirr for f→0 can be interpreted as a transition temperature separating the reversible vortex-liquid and the irreversible vortex-glass phases.