Wow... that's a weird one! (So's the tower being overloaded by resting birds! Wow!)
POSSIBLY, there may be a capacitor or insulator in the tuning unit that has a crack... and the moisture gets into it, causing the problem. This can also happen to the tower base insulator. (I hope not!!)
There also could be critter nests in places where the moisture wets the nest and de-tunes something. One station I had worked for years ago, had a mouse build a nest INSIDE one of the coils in the tuning unit! Once evicted, the stations parameters returned to normal.