The duration of the quasistationary states (QSSs) emerging in the d-dimensional classical inertial α-XY model, i.e., N planar rotators whose interactions decay with the distance r_{ij} as 1/r_{ij}^{α} (α≥0), is studied through first-principles molecular dynamics. These QSSs appear along the whole long-range interaction regime (0≤α/d≤1), for an average energy per rotator U<U_{c} (U_{c}=3/4), and they do not exist for U>U_{c}. They are characterized by a kinetic temperature T_{QSS}, before a crossover to a second plateau occurring at the Boltzmann-Gibbs temperature T_{BG}>T_{QSS}. We investigate here the behavior of their duration t_{QSS} when U approaches U_{c} from below, for large values of N. Contrary to the usual belief that the QSS merely disappears as U→U_{c}, we show that its duration goes through a critical phenomenon, namely t_{QSS}∝(U_{c}-U)^{-ξ}. Universality is found for the critical exponent ξ≃5/3 throughout the whole long-range interaction regime.