Sounds like bad design. Are the garages sitting above the bottom of the driveway? Where I live all the driveways that slope to the garage are built to have gradient on the driveway to help water runoff the sides (onto soil) abd before the driveway meets the garage there is a concrete slab that slopes up into the garage. The surface of the garage is a few inches above the bottom of the driveway.
The trouble is leaves, and when it snows a foot or two, the slush clogs any attempt at drainage.
Putting 1/4" steel mesh over the grate will at least make the leaf clogs visible so you can clean it.
When it snows heavily, you'll need to proactively shovel the drain clear, and clear the snow between the garage door and the drain.