Mine does fine as well in the North Texas areas and border OKLA...
I always park my trailer so the back is just a inch or so lower than then the front. This helps the run off go to the back side of the trailer. I have also seen some folks applying dicor to make a dam like thing to route the run-off water to the side rain gutter to keep the run off away from the rear window area.
Here is a pictorial of a typical air conditioner install. I suspect your 14X14-inch roof seal needs inspection. You can look up in the bottom section and see this foam gasket. It should be depressed about 1/4-inch all the way around it. You can also see the four long bolts that hold the top half in place - I have re-adjusted mine on several occasions as I guess the roof seal seal gasket starts losing it firmness.
You might look up in here on your next high humid camping. This is the only place I have ever seen water getting into the trailer from the roof mounted air conditioner...
On my OFF-ROAD POPUP with the fabric walls and tent ends I sometimes get a lot of condensation in high humid nights. Nothing worse than waking up with water dripping on your nose from the metal rails inside the tent bed. The fix for us on this problem was to keep a fan running all night long inside the trailer.
Roy Ken