There is an extensive list of possibilities for why your cockatiel keeps her eye closed most of the time. Some possibilities include bacterial or viral infections, trauma to the eye, inflammation from a foreign object stuck in the eye, tumors or cysts on the insides of the eyelids, pressure inside or behind the eye from an underlying disease process, etc. However, when a bird keeps one or both eyes closed it is usually an indication of pain (in the case of trauma) or poor health. Whether the problem is curable or not can only be determined once an evaluation and diagnosis of the problem has been made. I strongly suggest you take your bird to an exotic species veterinarian for a physical exam. Your vet will be able to use special tests and diagnostic equipment to determine the cause of the eye problem and offer you treatment options.