Precipitation is the one special case for which the original spatial coherence is lost in the downscaling process. Note however that the monthly means exactly equal the original monthly means (to within 0.5%), and that the internal consistency between precipitation and other highly related variables (lwdown, swdown, qair, etc.) is preserved (see Fig. 3, Kumar et al. 2012). However, the spatial pattern is lost. If spatially coherent precipitation is a firm requirement for your purposes there are other dynamic and semi-dynamic downscaling approaches that you can refer to, and will produce spatially coherent downscaled results.