Welcome from OHIO!!! How to fix the issue of rolling down window and then rolling it back up to have water on it.... Simple.... Leave window up... Just playing with you there (sorry if you took offence to my joke, didnt mean any harm).
Now, on a serious note, it sounds like you have a seal that is leaking. Is it like that on 1 door or both? If it is 1 door it is possible that the seal around the top to door is bad, or possible bad top. Pull of the door panel as to whichever side is holding water and then sit inside car while friend sprays water from garden hose. Let us know where your leak is.
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