The paper "Rainwater chemistry in the North Western Himalayan Region, India", published in Atmospheric Research 104-105 (2012) 128–138 may be interesting for you.
High altitude long distance atmospheric transport of acid precursors has been well-documented for Europe, e.g. from Western and central Europe to Scandinavia.
Hence I suggest checking whether your unpolluted rural region may be located downwind of an industrial centre that relies on fossil fuels for power generation etc.
In coastal locations diesel combustion from heavy ship traffic may make an important contribution to such precursors as well, because these fuels can have relatively high sulphur contents due to a lack of regulations.
This discussion goes far way back. Junge pointed out in his classical work 'AIr chemistry and radioactivity' (1963) that the pH of unpolluted rain can vary to a large degree just based on naturally occuring concentrations of ammonia and sulphur dioxide. In 1982 Charlos and Rodhe presented a thorough paper on this subject (Factors controlling the acidity of natural rainwater, Naure 295, 683-685). They demonstrate that the pH of natural precipitation can be somewhere in het pH range of 4 to 8, dependent on the circumstances.
the acidity of rainwater increase not only due to the high acidic components but also low basic components like calcium and magnesium. if the area is almost dust free then a minimum amount of sulfate or nitrate can make the pH of rainwater acidic (here i mean to say lower than 5.6)
Unpolluted rain in the atmosphere has an acidic pH (if unaffected by pollutants such as sulphur dioxide and oxides of nitrogen) and the acidic content of natural rainwater is largely caused by the greenhouse gas (carbon dioxide or CO2). Historically, the pH of rainwater was 5.68 (before 1800) and dropped to 5.62 (1800 to 2007) and projected to drop further to 5.49 (2100) due to rise of CO2. CO2 is dissolved by reactions with rain droplets, and the hydration of dissolved CO2 follows to give carbonic acid, the form in which CO2 occurs in rainwater.
Robert A. J. Bogan & Shigeru Ohde & Takeshi Arakaki & Ikuko Mori & Cameron W. McLeod. 2009. Changes in Rainwater pH associated with Increasing Atmospheric Carbon Dioxide after the Industrial Revolution. Water, Air, & Soil Pollution 196 (1-4): 263-271.