You need to do weights, the more lean muscle fibre your body has, the more bodyfat will be used as fuel.
Doing sit ups will not get rid of mid section fat. Also, if you've had children, (presuming you're female), then pregnancy can cause the muscles to become weak, plus where the skin has stretched to accomodate the growing baby, you may have poor elasticity.
It can be possible to lose this area or improve it, but it's not easy and most people aren't willing to do the amount of exercise necessary to see the reults.
Also, you might want to consider, that if you are menopausal or have been through it already, then it's quite common for women to accumulate fat in that area.