The attachment of water molecules onto size selected protonated water clusters has been experimentally investigated. Absolute attachment cross sections are measured as a function of cluster size, collision energy, and initial cluster temperature. Although thermal evaporation is ruled out in our experiment, attachment cross sections become significantly smaller than hard sphere cross sections as the collision energy increases. This feature is attributed to a transition from adiabatic to nonadiabatic regime. It is shown to be due to a dynamical effect: as the collision duration becomes shorter than the typical time required for collision energy redistribution into clusters internal energy, the attachment probability is reduced. We relate this typical time to the period of the main surface vibrational mode excited by the collisions. This hypothesis is further supported by results obtained with deuterated water clusters.