My heater core doesn't leak because it loses all of the air?!
Where, from the core or your connection?
I just assumed that it was bad when I originally described the symptoms and everyone here said "Oh yeah, your heater core is definitely bad, just bypass it!"
And what were they? I have a short memory. 
The bypass resolved it??
I drowned it under a brick today. After twelve hours I could not see any additional bubbles. I inserted the plug and Schrader valve, bolted on the brackets, pressurized it, and there were some slow bubbles coming from the bike bump itself, so I disconnected it. There were not any visible bubbles, but when I returned a couple of hours later all of the air was gone.
I was out at 06 working on it again, but when I removed the first nut it fell into the depths of the engine bay. I absolutely could not find it. I poked around with a flashlight and magnet on an extension. I poked around with my leaf blower. I lowered it and shook the car as much as possible.
Nothing.
You have to turn it upside down and shake.
I had a huge knot in my back, so I went inside, took ibuprofen, and laid down for a while.
It didn't seem to get any better.
You forgot the hot shower and the ice! I play a doctor on the internet.
I went back out and did about the first seven pages of instructions. Now I just need to remove the center panel, disconnect some cables under the steering wheel, ten bolts, seven nuts, twenty-eight screws, two brackets, and three pieces of trim.