Most likely is an accumulation of wear at the bearings/crankshaft. The oil pump is bound to be worn, too.
When the oil is cold, it has more viscosity so will give you a higher pressure reading until the oil is fully heated up. Once the oil thins out from heat, the losses at the journals, pump, and throughout the engine are great enough that the pump cannot keep up w/it, so the pressure will tend to drop.
You might try a heavier weight oil as a temporary measure until you can go in and rebuild it.