That is one of the major dangers of abs exercises. Everybody does them in hopes of losing fat in the midsection, even though it is the least effective thing to do for that. What many guys will forget about, is that you need to have a balance between the muscles in the lower back and the abs, and when you train your abs excessively (and I mean it - there is no need to train them that much), they ignore completely their lower back.
Also, there is a possibility of a poor form, which can also contribute to injuries. Therefore, if you are trying to lose fat, do other exercises, and leave the abs for some time. You will benefit much more from that, and perhaps the lower back will stop hurting you that bad.