A door, any door is a compromise. It has to be loose enough to
open and close, yet, tight enough to keep the wx outside.
If the door is mfg correctly, it should have an ogee cross section
where the sections mate top and bottom. This is such that the
front of the joint is lower than the back of the joint. If in fact you
have a door made that way there should be little or no intrusion
of rain, unless it is wind blown and then it will leak no matter the
construction. Most times, as suggested above, the slope of the
landscape, driveway, apron, or whatever, should be downward
away from the house or garage, and is a detail easily overlooked
by contractors; " Yeah, I looked at it and it's OK, just keep working."
At home, living on an island, we had a raised floor in the garage.
1.5" higher than the apron, and with the doors facing west (into the
prevailing wind) the floor stayed dry as long as the tide wasn't too high.
If I were you, I would consider an overhead shed roof in the front of the
o/h door, with a gutter and leader. It may not be to your astetic liking, but
it just may help the situation.
Uncle Bob