I don't think it's a nasty virus if it's been going on for a year. I'd also work to strengthen her immune system with a really good, comprehensive, liquid supplement. I think Reliv Kids' NOW is the best. It might do the trick with the fevers and it certainly will help her get enough nourishment, which is a good thing overall. Kids don't eat well, and for kids who don't absorb nutrients completely, chronic problems can occur. Besides, our food is way down in nutrient levels due to pollution and growing techniques and the way they gas the produce just to make it last longer. So even good eaters are nutrient-deficient. So says the American Medical Association - in 2002 they recommended that everyone supplement, and they said liquid is the best (ideally, a powder you mix in liquid, not a pre-mixed product which loses potency).
The temp may not be high, but it's recurrent and it's affecting her behavior. I wouldn't ignore it. If the nutrition doesn't take care of it and if it continues, I'd also try another doctor and get a work-up.