Technically, every model is in danger of falling apart at some point. Even polystyrene models eventually degrade. I recently started restoring an old model from the 1960's. It was made of styrene, so it's parts must be reinforced due to its fragility. The parts crack in places new parts usually wouldn't.
One of the most durable model materials currently being used is stainless steel sheet. Other materials include wood, aluminum (aluminium), brass, glass and polycarbonates. Basically, any long-lasting material you can find for real items is a good model material.