The Odin space telescope has monitored the H2O (110-101) line in Jupiter's stratosphere over the 2003-2009 period. When comparing these data with previous spectra obtained with SWAS and Odin over the 1999-2002 period, we see no significant variations in the line-to-continuum ratio of the H2O line over the whole period. We have however tentatively identified a decrease by ∼15% of the line-to-continuum ratio between 2002 and 2007-2009, indicating that there was less H2O in the stratosphere of Jupiter in 2007-2009 than anticipated. We have tested the IDP (interplanetary dust particles) and SL9 (Shoemaker-Levy 9) 1D time-dependent models presented in Cavalié et al. [2008, Observation of water vapor in the stratosphere 613 of Jupiter with the Odin space telescope. Planetary and Space Science 56, 1573-1584]. We present a series of scenarios that lead to satisfactory fits of the whole data set (1999-2002 and 2003-2009 periods) based on IDP and SL9 models. The evolution of Jupiter's stratospheric H2O that we have tentatively observed has however to be confirmed by Herschel/HIFI observations. If the decrease of the line-to-continuum ratio is confirmed by future observations, it would be a direct evidence that Jupiter's H2O comes from SL9. In addition, this study shows that new constraints on Jupiter's eddy diffusion coefficient profile could be obtained (in the pressure ranges that are probed) from the monitoring of SL9 species in its stratosphere.Read less <