The reasons why some women may not have a period on the pill are pregnancy and thinning of the endometrial lining caused by the pill.
What do I mean by thinning of the endometrial lining? The top layer of the endometrium is the innermost lining of your uterus that you shed as a period. Think of the lining as grass growing. The grass grows during a menstrual cycle and your body triggers the grass to be shed cyclically in the form of menstrual flow or a period.
The birth control pill inhibits the grass from growing by minimizing the amount of estrogen that your body produces (Think of estrogen as water.). If no grass is growing then no grass will be shed. If the endometrial lining is really thin then there is no endometrium to be shed and you will not have a period.