Sounds like you might have problems with the reservoir. If the seals are poor the pressure to bleed the brakes will not be maintained and you will find it tricky to get all the air out. As a rule when you pull the plunger on the top of the reservoir up it should stay up and you can then bleed the brakes as plunger is a piston acting down on the brake fluid via a spring and some brake seals. It might be the master cylinder bore is worn or the flexible hydraulic hoses are weak.
The Appia Consortium has most of the seals you might need as well as new hoses.
Clarkey