Truck Battery Dies if left sitting for more than a day, battery is brand new but the old battery did the same?

Something is causing the battery(s) in my truck to die if I let it sit for more than a day, I replaced the old battery but the new one is doing the same thing, the alternator was tested and is fine, the truck is a 1981 Chevrolet C-10 I6 4.1L, also I live in Utah so it's been 19 and below here recently, any help?