You brake system has a line cut-off valve on the driver firewall. This valve is to stop fluid from leaking out completely incase of a line being ruptured. It has one side connected to the front brakes and the other connected to the rear brakes. Inside is a piston which, when centered allows brake fluid from one part of the master cylinder to go to the front brakes and fluid from the other to go the the rear bakes. The pressure must be equal on both sides of the piston. Should the pressure fall in one circuit the plunger moves to block that circuit and only the the non-broken circuit will get fluid. This maintains at least some braking.
If you open a bleeder and push the brake pedal down quickly you will cause the piston to move and block the circuit. On the second push, you only pressurize the other circuit and the one with the bleeder open will be blocked keeping it from bleeding.
You need to insure that the plunger is centered. The plunger not only blocks a leaking circuit, it has switch contacts that light the light on the dash saying one circuit has failed. You need to open a bleed valve on the unblocked circuit, with the blocked circuit bleed closed and depress the brake pedal until the light goes out. Push too far and the piston move the other way and the light comes on again. Only push until the light goes out. Then close the bleeder. This will center the piston. Now go back to bleeding the brakes but only open the bleeder a little bit and push the pedal down slowly so the safety plunger does not move.
Remember this when changing brake pads . When new pads are installed there is some space between them and the disk. Slowly push the pedal down and never all the way to the floor or you will probably throw the safety piston.