Power generation from renewable energy sources, in particular solar photovoltaics (PV), has become extremely attractive thanks to its very low levelized cost of electricity (LCoE). In desert-like environments, the energy yield is drastically reduced due to dust accumulation. While effective and affordable cleaning strategies can be implemented in large, MW-size PV power plants, soiling remains an economic and logistic challenge. In this article, we analyze the soiling loss rates of PV modules for different tilt angles measured during a period of 15 months in the Western Region of Saudi Arabia. We observe a strong correlation between weather parameters like humidity and wind speed and the mechanism of dust accumulation. Our measurements show that, for specific weather conditions, soiled modules undergo a partial cleaning process. As a consequence, and for the first time, the soiling loss rates are shown to have a clear dependence on the current soiling state of the modules, with clean modules soiling twice as fast as soiled ones. This dependency is a key for predicting the correct cleaning frequency of a PV power plant. Finally, the results obtained for vertically mounted modules (90 deg), where dust accumulation is negligible, point to a favorable case for the use of bifacial PV modules.