We present multi-epoch Very Long Baseline Array (VLBA) H$_2$O maser observations toward 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 $sim$ 10 yrs, measuring their radial velocities and proper motions. The H$_2$O masers in VLA 3, the most massive YSO in AFGL 2591 ($sim$ 30--40~M$_{odot}$), are grouped within projected distances of $lesssim$ 40 mas ($lesssim$ 130 AU) from VLA 3. In contrast to other H$_2$O masers in AFGL 2591, the masers associated with VLA 3 are significantly blueshifted (up to $sim$ 30 km s$^{-1}$) with respect to the velocity of the ambient molecular cloud. We find that the H$_2$O maser cluster as a whole, has moved westwards of VLA~3 between the 2001 and 2009 observations, with a proper motion of $sim$ 1.2 mas yr$^{-1}$ ($sim$ 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 $sim$ 0.7$$ ($sim$ 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.
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