I have been having this same problem since I started working on the break system. It's a 67 Malibu with drums all around.
Everything is new except the prop valve. I have tried two different masters and bench bled them. I have gravity bled, pedal bled, and pressure bled with the same results.
I get good pedal at first then about 10 times of breaking I lose almost all of my pedal.

I have checked and rechecked for leaks because when I go to bleed again there is always air in the right rear. When I check the master there doesn't seem to be any loss of fluid. Also today I tried to gravity bleed again and got air out of the line again. But the strange thing that happened was it bled for about 10 min. then quit. I didn't get a drop of fluid out.

How can I be getting air in the line without noticing a leak somewhere? What should I do next?
Thanks
John

Have you replaced the rubber hoses? how are the wheel cylinders ?

Yes. Everything is new. Last night tried to gravity bleed again at the right rear wheel for about an hour. Had to quit because I ran out of break fluid.
I might need to buy a 55 gal. drum.

Check to make sure all of your flared fitting are seated properly. They may look OK and the fitting connector my look as if it is screwed down properly but if they are not seated they will leak. The only way to check to see if the fitting is leaking is to listen for an air hiss. Put your ear to the fitting (as close as possible) and have someone pump the brakes. If you hear a hiss, take off the fitting, check the flared end for scratches or gunk and put back as squarely as you can. Just a suggestion as I had the same problem and it was the fitting connection.

Charlie,
Now that you mentioned it the rear lines were already on when I got the car. They were new but when I changed the wheel cylinders the line going into the right rear cylinder seemed to me to be to long. In other words I don't think the flare is seating against the fitting conector. Do you think that may be my problem?

Very well could be. Maybe you should take apart the fittings and re-seat. Might even re-flare the end if you have the tools.

Hello Everyone,
Since my last post here is what is going on. I installed a new master (not rebuilt), new distribution block, and new lines going from master to dist. block. I also moved the rear line away from the headers. New wheel cylinders.
The problem is still the same. I am getting air someware in the rear lines. Tested the master again and it is fine. I have no problems with the front.
As I said before, When I get done bleeding all 4 wheels I get hard pedal for about 5 to 10 pumps and then the pedal goes soft. Took off rear drums and seen that the rears are not breaking. Then I rebled the rears again and sure enough air is back in the rear lines.
I am ready to pull out the little hair I have left. Can anyone walk me through some sort of procedure to find out what is going on?
Thanks
John