What kind of soil does it run through?
Lime, peat, ?
If the power plant is using water for cooling or steam generation is it treating it with anything, like de-scalers or water softeners?
There are quite a few possible causes. But if the plant is using acids to clean boiler scale or if the river is running over acidic rocks or through swampy ground those might be sources of acidity.
If the water levels are low the plant might be using a much higher proportion of the water in the river. It is also possible for the acidity levels to be higher if it is taking more of its water out of swampy ground. These could be affected by flow rates because of lower dilution effects.
Are there any other sources of acidic inputs like run off from livestock yards, septic overflows etc?
It is easy to point a finger at the plant, but hard to demonstrate it.
What is the pH upstream of the plant at their intake and below the plant at their outflow?
That might give you an idea if they are a source or not.