Some good thoughts by the posters.

Is the painter sealing everything? Is the weather stripping in good
condition?

Also, there may be a problem with the sill, in that it isn't shedding
the water. I've seen windows installed in a way that the sill actually
slopes back toward the house. [This is an extreme example, but the sill
should slope down away from the house].

One last thought - even when using a solid color stain on siding, I
always used paint on the smooth, harder window/door trim. This may be
an option for you, but you should first figure out why you're having
the problem.