We present multi-epoch Very Long Baseline Array (VLBA) H2O maser observations towards the massive young stellar objects (YSOs) VLA 2 and VLA 3 in the star-forming region AFGL 2591. Through these observations, we have extended the study of the evolution of the masers towards these objects up to a time-span of ~10 yr, measuring their radial velocities and proper motions. The H2O masers in VLA 3, the most massive YSO in AFGL 2591 (~30-40 M?), are grouped within projected distances of ?40 mas (?130 au) from VLA 3. In contrast to other H2O masers in AFGL 2591, the masers associated with VLA 3 are significantly blueshifted (up to ~30 km s-1) with respect to the velocity of the ambient molecular cloud. We find that the H2O maser cluster as a whole has moved westwards of VLA 3 between the 2001 and 2009 observations, with a proper motion of ~1.2 mas yr-1 (~20 km s-1). We conclude that these masers are tracing blueshifted outflowing material, shock excited at the inner parts of a cavity seen previously in ammonia molecular lines and infrared images, and proposed to be evacuated by the outflow associated with the massive VLA 3 source. The masers in the region of VLA 2 are located at projected distances of ~0.7 arcsec (~2300 au) north from this source, with their kinematics suggesting that they are excited by a YSO other than VLA 2. This driving source has not yet been identified.
