Hi Fitness Mom! Are you talking about core work or traditional ab work with crunch variations? If it is core work, it would be normal to experience fatigue in your back because you are using and fatiguing your back muscles while doing core work. In this case I will say that do only what you can and gradually try to work at holding your positions slightly longer every couple of workouts. It will eventually get easier as your back strengthens.
If you are experiencing excessive back stress on traditional ab work, then it could be that your back needs to be strengthened. Without actually seeing you perform your exercises it would be hard for me to say that your form could be the reason for the discomfort. But if you are constantly feeling these exercises more in your back and you feel pretty confident that you are doing them the exact way you are viewing them, then I would say that you would benefit from strengthening your back with some back exercises that we include in our weight training workouts. Try incorporating one to two back workouts (about three days apart) in addition to your abdominal/core training.
Good Luck!