Bleeding trailer brakes

I am not sure what I am doing wrong. The disc brakes on my tandem axle trailer were no longer working. After checking for leaks and not finding any and the brake fluid reservoir was full, I assumed I likely had a bad master cylinder/coupler or a bad reverse switch. I tested the switch and it appeared to be working so I ordered a new coupler, had it painted to match and installed it. New coupler also has a new reverse switch.

I was bleeding the brakes (which I have done 20 times before on other vehicles/trailers) by not plugging in the trailer (reverse switch), "pumping" the master cylinder (with my truck) with the trailer wheels blocked, holding pressure, running to the back (starting with the furthest wheel from the coupler) and making sure I never ran low on fluid. I recognized I likely needed to bleed these lines a lot as I had to pull some of the lines out to replace the coupler plus I had a new coupler which would make sense.

For some reason I couldn't bleed all of the air out of the system. I did this for 4+ hours and couldn't get the air out. I was able to get some pressure on the brake lines but not enough for the brakes to really stop the trailer. I made sure I never ran out of fluid in the reservoir (by filling it up after every bleed) but I simply couldn't get the pressure up.

I had bought a power bleeder before I started this project but the design of the reservoir (no threaded cap - just a rubber plug) made the power bleeder useless.

Any advice? I can't find a leak anywhere in the system - could there be a small leak that doesn't leak oil but lets air in? Maybe I just need to keep going and it will eventually build pressure?