The slow draining is from the initial puncture, and it's often better to let it drain slowly that way rather than take a whole bunch really fast. The draining will sometimes make them feel better for a while as it relieves the pressure in the abdomen, but it will recur since the underlying condition is still there. It could be infection, a cancer, or organ failure, those are the most common causes of ascites, and the heart is failing. You may be able to get her stabilized now, but the long term prognosis is likely poor.