One possible reason why your Daewoo Matiz 800 SE has difficulty starting after riding a few miles is an issue with the fuel system. The fuel pump may be failing or not delivering enough fuel to the engine. This can cause the engine to run lean, which can make it difficult to start. Additionally, a clogged fuel filter can restrict the flow of fuel to the engine, making it harder to start the car. Another possible explanation is a malfunctioning ignition system caused by a bad spark plug, ignition coil or distributor cap. If the engine is not getting enough spark, it can make starting difficult after the car's been driven for a few miles. Lastly, issues related to the engine's cooling system, such as a faulty thermostat or a blocked radiator, may cause the engine to overheat when driven, making it harder to start after the car is shut down. If the car is having trouble starting repeatedly, it may be best to have a mechanic diagnose the issue and perform any necessary repairs.