How is it possible to use up the water in a region?
This is a really complex problem and would require a really detailed explanation about atmospheric circulation, meteorology and hydrology.

The short answer to your question is that water is going somewhere else. If you look at the studies about moisture recycling, among the others van der Ent et al 2014 or 2010, you can see that the precipitation that generates from locally generated moisture is just a minor fraction, and usually is higher in very wet areas. So, your assumption of the "few hundreds kilometers" is generally wrong. Considering a very wet area like the Amazon forest, you can see that the moisture locally generated is the major source (about 70% in quantity) of the precipitations in South-Eastern Brazil. This is due to the atmospheric circulation and the topography of the continent.



Source van der Ent et al 2010.

To fully answer your question, both in case of precipitation and in the case of underground percolation, the water used locally in agriculture or other uses, would go to contribute to other drainage basins (both in the cases of surface water and underground aquifers).