Originally Posted by JeffN
I'd be surprised if it were punctured and there is no flashing.
If you're sure there is no flashing, that could be where the water is getting in. Low-slope, carport (or any other) roofs need properly-installed flashing at their intersections with abutting walls or sloped roofs. With the vertical/upright legs tucked under the wall's siding or shingles, and the horizontal legs remaining on top of the membrane, water should have a hard time finding its way in and leaking.