360 Oil Pressure Issues

I have a 360 installed in my 65 Barracuda and it has been in the car for about 2 years now. I do not get to drive the car as much as I wish I could, but ever since I started taking the car out on the town I have noticed that my oil pressure gets quite low. When I first fire up the car oil pressure jumps to 30psi and holds steady for 15-20 minutes. After the 15-20 minutes the oil pressure begins to slowly drop off at a steady rate until it pretty much is at 0. The pressure will jump up if I throw some extra RPMs into the motor, but even then it only jumps 5 psi up and instantly goes back down. I am lost on what the issue could be. I bought the engine pre-built, but I tore it down to just a short block. It has a new stock oil pump, pickup, and pan. I think I might try a new gauge to see if possibly my current one is faulty. But other than that I am completely lost.