Why does my Conure chew her tail when I'm away from home for a few hours?

I have a 8 month old Pineapple Green Cheek Conure since she's been weaned. For the past 2 months or so, and I've noticed tonight it's gotten worse, that if I decide to go out to a movie, out to eat or to town for a couple of hours, when I return home, she's chewed up the tips of her tail. I'm home with her all the time, besides the fact when I have to go out, and sometimes when I go out, I'll take her with me in the car, because she loves car rides. But, I went out to celebrate my birthday today leaving around 6-7 o'clock that evening. By the time I got home around 12:30-1AM, she had the ends of her tail chewed. She has plenty of toys, and a large cage. She even has preening toys to keep her occupied for when she wants to cut her little fits like that. I also notice, when she doesn't get her way, and gets mad, she will also chew on the tips of her tail as well. It kind of reminds of me a child throwing a tantrum. I'm just at a loss on what to do, because I have done EVERYTHING in my power to attempt to solve this problem, and I can't take her with me where ever I go all the time.