Clutch system getting air

I did not see an area to post about anything transmission related, so I'm posting here.

I started getting air into my clutch pedal a while back. I did some research and discovered that since the system wasn't losing fluid, the issue was likely the master clutch cylinder. So I replaced my master cylinder and bled the system. After a day or two, air started getting back into the system, so I bled it a few more times. This is still happening and I have now bled the system about 10 times. Any ideas? I've read through other forums about this same issue on different cars, and concluded that no fluid will leak out of the system unless a slave cylinder is broken. Since I'm not losing fluid, I haven't looked into the slave cylinder as a possibility. Can someone let me know if my conclusion is correct that the master cylinder won't leak fluid but the slave will?