I'm not familiar with storm windows attached to the outside of a travel trailer. Could you provide photos? Check the window tracks on the exterior for debris blocking the drain holes. In addition, you could buy some butyl rubber caulk and apply a bead to the top edges of each window frame.
The windows are usually held in place by a bunch of screws on the inside trim that goes through to the outside rim. A gasket of butyl rubber tape is usually applied to the window exterior trim and then tightened against the outside of the trailer walls. It does deteriorate over time. If you removed the screws, someone on the outside holding the window in place as the last few are removed, would allow Removing the window, cleaning off the old caulk, and applying new would be the ultimate way to go.