has she been laying? is her abdomen swollen? she could possibly be laying internally and there is a large amount of liquid in the abdomen. have you noticed if the abdomen is swollen or warm to touch. its likely she has an infection inside the abdomen. this is my best guess. how much liquid comes out? does it have a smell? is it always clear? this if it is what's going on is brought on from laying internally and called egg yolk peritonitis. egg albumin and yolks accumulate in the abdomen. causing infection and an accumulation of fluids in the abdomen. some has been successful in draining the abdomen with a syringe. I'm not sure this is what is happening with your bird but peritonitis comes to mind if liquid is draining from the vent area. not sure though. perhaps someone else has another possibility?