How is air getting into my lines?

Try adjusting the (front) shoes up nice and tight and then bleed them. You might have trouble with brake hardware, IE shoe return springs, something like that. The idea is this:

Drum masters have a residual valve which is supposed to keep a small positive pressure in the system. (Why I don't like vacuum bleeders). This is to keep air from coming INTO the wheel cups during the return. The wheel cups MUST be spring return via the brake return springs to keep the cups expanded. If the master tries to return, and if pressure drops off in the system, air can come in around the cylinder cups.

Some sort of damage in one cylinder could certainly be a problem, a burr on the cylinder wall or some such.

^^^What he said^^^

Any drum system I have ever had trouble bleeding has always turned out to be a bad wheel cylinder. Ive also seen on 2 occasions, the spring in the middle of the two rubber cups inside the wheel cylinder, missing. Also, the residual pressure valves can cease to operate if the system was left dry and open to elements too long.

Rusty is right about the cheap chinese knockoffs. I rebuilt my original wheel cylinders. The kits were like $5 or $6 each from Rockauto. Now I can't say the kits weren't made in china, but I know my quality control is a hell of a lot better!