Context. The comet Shoemaker-Levy 9 impacted Jupiter in July 1994, leaving its stratosphere with several new species, with water vapor (H2O) among them.Aims. With the aid of a photochemical model, H2O can be used as a dynamical tracer in the Jovian stratosphere. In this paper, we aim to constrain the vertical eddy diffusion (Kzz) at levels where H2O is present.Methods. We monitored the H2O disk-averaged emission at 556.936 GHz with the space telescope between 2002 and 2019, covering nearly two decades. We analyzed the data with a combination of 1D photochemical and radiative transfer models to constrain the vertical eddy diffusion in the stratosphere of Jupiter. Results. Odin observations show us that the emission of H2O has an almost linear decrease of about 40% between 2002 and 2019. We can only reproduce our time series if we increase the magnitude of Kzz in the pressure range where H2O diffuses downward from 2002 to 2019, that is, from ~0.2 mbar to ~5 mbar. However, this modified Kzz is incompatible with hydrocarbon observations. We find that even if an allowance is made for the initially large abundances of H2O and CO at the impact latitudes, the photochemical conversion of H2O to CO2 is not sufficient to explain the progressive decline of the H2O line emission, which is suggestive of additional loss mechanisms.Conclusions. The Kzz we derived from the Odin observations of H2O can only be viewed as an upper limit in the ~0.2 mbar to ~5 mbar pressure range. The incompatibility between the interpretations made from H2O and hydrocarbon observations probably results from 1D modeling limitations. Meridional variability of H2O, most probably at auroral latitudes, would need to be assessed and compared with that of hydrocarbons to quantify the role of auroral chemistry in the temporal evolution of the H2O abundance since the SL9 impacts. Modeling the temporal evolution of SL9 species with a 2D model would naturally be the next step in this area of study.