I'd check back with your surgeon. At some point the risk of keeping the drain in outweighs the potential benefit. If you develop a seroma this can be removed by a simple aspiration. Sometimes the drain itself can promote more fluid formation.
Drains after abdominoplasty do not usually remain in for a month. If the drains are not resolving the fluid then other forms of resolving the fluid should be sought.
It is rare to need drains for such a long time. In very very rare case I have kept drains for longer than 2 weeks but after a while the risk of infection along the drain site outweighs the benefit of keeping them in. If you do need drains for some reason, removing them may lead to a fluid collection (seroma) that will require a needle to drain them at a later date.
If you still have drains at a month, I assume you are draining a significant amount of fluid. It is unusual to require drains for a month, and I would worry about possible infection from the drain site. Nutritional supplements are necessary in your case, because for a month you are losing a substantial amount of calories in the drain fluid. A workup from a nutritionist may be helpful. Removal of the drain may also stimulate a decrease. Remaining fluid can be removed with a needle in the numb paert of the skin. If the drain is removed, a culture of the drainage and drain tip would be valuable.