I got down to 9% bf for a natural competition I did last year while on bc. My period stopped when I hit 10% bf. This happens to most women when they get at or below that level of body fat. In general this is not a healthy thing to maintain - if the estrogen is cut off for extended periods of time (e.g. bodybuilding and also in anorexics/bulemics) bones can become more brittle - loss of menstruation can affect the body's ability to absorb calcium, leading to easily fractured or broken bones and eventually osteoporosis. (Ref:
http://women.com/fitness/olympics2000/goingthedistance/index.html)
I checked w/ my OB-GYN about estrogen-related fat retention as a result of my bc, and he said there should be very little effect from it because it was a very light estrogen/progesterone combination. I did go off it in February of this year and didn't notice any reduction in fat loss as a result. I only experienced some slight increase in cramps etc. the first month I was off. Generally it seems to take 3 months for a body to adapt to changes related to estrogen levels (just an observational number). If you read some of the posts on this topic, many women did experience significant fat retention while on bc, losing a large % of it when going off and moving to other bc alternatives like an IUD. Note that the IUD has issues, so consult your doc if that's the route you wish to take for birth control.
Hope that helps. For a few % bodyfat, you might try increased morning cardio on an empty stomach to reach your goals before giving up the advantages of birth control pills. However if you are having trouble with the pill anyway, you might check w/ your doc about a lower/different dosage pill, or just go off.
~ sassy