Depending on the type or manufacturer of composition shingles diffrent measures of maintance may be required. For instance a 20 year three tab composition material is more likely to suffer damage due to high winds. Dimensional, also known as archetictual composition, do much better under the same windy conditions. They don't blow off as easily.
Most of the issues that we find with this kind of roofing material is incorrect installation. Usually around flashing penetrations, such as chimneys, skylights, & vent pipe flashings. Other then the afore mentioned a composition roof is fairly low maintance and will typically last as long as the manufacturer's warranty stipulates.