Unable to bleed clutch after new slave cylinder installed

Replaced a bad clutch on a 2004 Mitsubishi Lancer. I have been unable to bleed the slave cylinder after replacing both it and the master cylinder. I suspect either the slave cylinder is bad, or I put the incorrect throwout bearing in when the clutch was replaced. The slave cylinder is located inside of the bell housing

Another possibility is that you put the clutch plate facing the wrong way.

I hope not.
I forgot to mention that after I bleed the clutch, it is good for about 25 to 50 presses on the clutch pedal, and it slowly gets air into the system. I have had to use a vacuum pump to get the air bubbles out of the slave cylinder.

If air is getting in after you bleed then you have a leak.

Did you bench bleed the cylinder?

Provided you do not have a leak in the line that’s allowing air to be drawn in, chances are you either did not properly bleed the new master cylinder or you have a bad one. To bleed any MC, you must connect a feedback loop from the outlet to the reservoir and affixed so the feedback loop does not inject air into the reservoir. Short-stroke (25-30% of stroke) the MC several times until you start getting fluid out of the feedback loop then slowly increase the amount of stroke until you get to full-strokes which you’ll want to do about 10-15. Then, let it sit for 30 minutes and give it another 10-15 full strokes checking to make sure you don’t get any bubbles out of the feedback loop, if you do, let it rest again and repeat. If you get bubbles the second time around, the MC assembly is bad. That’s not an uncommon thing to get bad parts and it could very well be the slave cylinder is bad too, they can suck air around the shaft just as the MC can. BTW, that horsepucky about bleeding MC’s (any MC) with plugs in the outputs is just that, horsepucky! 99% of the time doesn’t work, and even if you get the delivery side of the piston to load with fluid, you’ll pump/vacuum your brains out trying to get all the air out of the system - use the feedback loops and save yourself the time and hassles.

There are no leaks.

I did not bench bleed the master cylinder, due to all of the contortions required to get it in place around the booster cylinder for the brakes.

I used a hand actuated vacuum pump to try and make sure the master cylinder was bled.