Went to press the brakes you'd realize that there were no brakes?

I started working on these brakes because occasionally when it would first start up, there would be no brake pressure. As you were reversing out of the drive way, you would forget and as you went to press the brakes you'd realize that there were no brakes until you quickly pumped it up. A post it was installed right above the radio reminding the driver to pump the brakes before taking off. The brakes would work perfectly fine after a few pumps. Again, this would only need to be done occasionally and nobody knew when or why. So I was tasked with just fixing it. I assumed master cylinder so I replaced it but now there are no brakes (as in no pressure when I press the brake pedal). I've completed about a dozen rounds of brake bleeding but I can't seem to get the air out of the system. I'm assuming that's why there's no pressure when I depress the pedal but I could be wrong. However, I'm not sure what else it could be. Any advice would be greatly appreciated.

P. S. I'm manually bleeding the brakes alone using a "spreader" tool to apply pressure to the pedal as I loosen the valve and close it once the fluid stops flowing. Then I release the spreader and reapply it then reopen the valve and so on. Repeating this about 5 or 6 times at each wheel. Every once in a while air will come out. When that happens, I'll repeat my process until I don't see any bubbles but the pedal doesn't seem to be getting any stiffer. I believe air is still trapped in the system but don't really know how to effectively remove it. Do I stay the course and keep bleeding it as I have been doing, should I try a different method, or am I wrong in thinking it's air in the system, that it's something else altogether such as a defective abs pump or broken brake line, etc? Thanks for your time.