The breast feeding will still affect your hormone levels...this will affect your periods and ovulaiton.
The mini pill is so named because it doesnt contain the same volume of hormones in regular pills.
The month is both cautionary and practical. The time it takes for (any) pill to work in any womans body is different for everyone. Generally spekaing, you need to wait a full cycle in order to make sure your hormones and body are responding the way they should be.
You will still get your period whilst on the pill. Getting your period isnt dependent necessarily of whether or not you ovulate (hence why just because you have your period again doesnt mean you are ovulating regularly. and why the mini pill becomes less effective, because the levels change and with personal variation, there is no guarantee or ability for the doctor to tell you when it will stop working.)
So when BF over time, your hormones levels change and allow your body to ovulate again, hence why the pill can become inaffective - the hormones in it are simply not strong enough to regulate your cycle adequately. Sort of like what happens if you are put on a normal pill that isnt strong enough.

Thats how my doctor explained it to me anyhow!

Have you looked into getting a Mirena fitted?
HTH