I had a similar issue with one door's outer belt line weatherstripping (not snapping into place and staying). Assemblyline door (all straightened correctly in the slots) and a NOS Service Part.
Once it pulled loose after raising and lowering the glass a few times (while fine-tuning the glass adjustments), I had to reach around the back of the window & regulator with a hook tool in hand and depress the several fasteners that actually HAD engaged into the slots properly (of the door).
This is not an easy task for most of us full-sized people!
With the weatherstripping fully removed again, I diagnosed the issues with the clip-fasters (were mis-shaped on the few that wouldn't stay engaged)...I carefully re-tweeked them to snap in correctly and re-installed the same weatherstrip.
I ASSUMED a New, un-used Ford Service Part wouldn't have had such an issue but there I was, doing the impossible (again).