I agree there is not much of a slope but there is some slope. It drops only a foot or two from where the water enters to pipe to where it dumps into the storm sewer. I can see where it enters the storm sewer and it seems to empty just fine in the summer. Im assuming a small amount of ice continually builds over the winter until it clogs the whole line.
I might also try flushing it with hot water a couple times a year to melt away anything that has built up??