The most likely cause of a car losing oil pressure when it warms up is a problem with the pressure relief valve, which regulates the oil pressure to ensure that there is enough pressure to circulate oil throughout the engine. When oil pressure is low, not enough oil is being distributed to the engine, potentially causing engine failure.
To a certain extent, it is normal for a car to have low oil pressure when first starting. However, within 20 minutes, the oil pressure should be regulated, and the needle on the oil pressure gauge should rest at the midpoint. If the oil pressure remains low, have the oil pressure relief valve inspected by a mechanic.
It is also possible that the oil pump is malfunctioning, which is responsible for regulating the flow of oil. The resistance to the flow of oil is what causes oil pressure. If the oil pressure is low, the fuel flow is low. This is a major problem that needs to be fixed immediately, since the engine needs to be lubricated adequately to function properly.
Other causes of low oil pressure include excessive bearing clearance, a blockage in the oil delivery lines, a worn crankshaft and air in the oil pump.