Yes it is a problem Lorne, except for roofs in some desert areas where evaporating water is part of the air conditioning design, and the roof is specially designed like a swimming pool. For the rest of us, standing water will lead to a premature ageing of the roofing material, whatever material it may be. This usually happens in a roof that has a central drain and the drain is placed near part of the structural support. As in the first drawing, when the building ages and things sag a bit, the drain becomes the high point on the roof, and puddles form. Drains should be placed in the centre of unsupported areas. In fact having a certain length of sloped almost horizontal piping will provide a bit of flexibility in the system that will keep the drain at the low point on the roof.
Aside from all of that, standing water is a terrific place to breed mosquitos. In the past, mosquitos were just a nuisance. Today, standing water can be life threatening. Mosquito borne diseases such as West Nile disease and Dengue Fever have reached North America and Hawaii. All standing water is a breeding ground for these deadly mosquitos. Hawaii has an active program to educate citizens and eliminate as much standing water as possible.
If you can install a drain at the lowest point or points of the roof, you won't have to rebuild the entire roof. Otherwise you will need to rebuild the deck of the roof, assuring a proper slope.