I wonder if she's really unhappy about having a cage-mate? My old cockatiel did the same thing. He was alone for 8 years and despised the female he was housed with after that. We eventually had to split them up and all was well.
A long shot is his food. My old cockatiel is not doing well at all. It's probably kidney failure from melamine (I hate China!) in a cheap brand of food I got at the grocery store one day while I was in a hurry. The manufacterer of the food is Wild Harvest, and several different bird foods and treats were recalled by the FDA in December last year. I didn't learn about the recall until the bag was nearly empty, and yes, the lot number was one that was recalled. The retailer never took it off the shelf and continues to sell this brand. I've not seen Wild Harvest carried at Petco or PetSmart, which is where I have always purchased pet food.
It is possible that your new budgie may have introduced a parasite to your old budgie. Could you bring a sample of your older budgie's droppings to have it analysed for parasites, giardia, and other protozoas. An exam wouldn't hurt also.