We monitored the 22 GHz maser line in the lensed quasar MG J0414+0534 at z = 2.64 with the 300-m Arecibo telescope for almost two years to detect possible additional maser components and to measure a potential velocity drift of the lines. The main maser line profile is complex and can be resolved into a number of broad features with line widths of 30-160 km s−1. A new maser component was tentatively detected in October 2008 at a velocity of +470 km s−1. After correcting for the estimated lens magnification, we find that the H2O isotropic luminosity of the maser in MG J0414+0534 is ~26,000 solar luminosities, making this source the most luminous ever discovered. Both the main line peak and continuum flux densities are surprisingly stable throughout the period of the observations. An upper limit on the velocity drift of the main peak of the line has been estimated from our observations and is of the order of 2 km s−1 per year. We discuss the results of the monitoring in terms of the possible nature of the maser emission, associated with an accretion disk or a radio jet. This is the first time that such a study is performed in a water maser source at high redshift, potentially allowing us to study the parsec-scale environment around a powerful radio source at cosmological distances.