Most flat roofs, when built correctly, will last for many years before they need any type of maintenance or repair. However flat roofs do have a bad name, which is unfortunately down to the way they are designed.
Flat roofs should never be installed geometrically flat. If they are flat, the rainwater will not run away from the roof and ponding may result. Ponding can also be a problem when the roof is made from inadequate materials which cannot support the roof structure leading to sagging. A pool of water which sits on the roof structure will invariably find its way through even the smallest imperfection, and the roof will leak.
The boarding on a flat roof should comprise of marine plywood or WBP plywood and have a run off gradient of at least 1 in 80. If the boarding on your roof is standard plywood or even worse chipboard, you are only asking for trouble in the future.
The standard roofing material for a flat roof is torch-on felt, which can be easily fitted to a roof in a mater of hours by a professional installer. It's worth noting, that when your flat roof material is replaced, building regulations now state that the insulation used in the roof should be brought up to current standards.