I can confirm that even with a new roof, if you don't go with the more expensive solution, sloping to the drain or gutters, it will quickly fail. We recently had one of our roofs redone with a bit of a slope, new gutters, and lots of insulation. The other roof was replaced about 8 years ago, and because of the water, failed very quickly. We had to have another specialist company come in to make repairs, but this reminds me to have them back before it starts leaking again. When we insulate this second roof, maybe we'll do a new roof at the same time.
Also, make sure you hire a contractor who specializes in flat/membrane roofs, and is highly recommended by friends and neighbors.