Sounds like she has been bounced around a lot with different handlers if she is in a lease at a large? barn. My gelding was very aloof when I got him, but once I earned his trust we were been bonded for life. I think a lot of arabs are one-person horses, and when not treated according to their personality, become indifferent and sort of shut off.
I also wanted to point out that this certainly can occur with other breeds too. I was at a barn where a lot of force was used with the horses and little regard was paid to their personality. Since they were mostly tb's, and having a bad experience with a mean tb myself, I began to think that it was just the breed. I now lease a tb who is wonderful and sweet. The difference: he is at a much better barn and has not had too many different riders. All in all, he has really changed my opinion about the breed and caused me to be much more open-minded.
I would just spend some time grooming and doting on her to show her that you recognize her as an individual and not just "a horse." As others have said, try to spend more time caring for her, and mix it up a bit to keep her happy being ridden. If you can get through to her, her personality will likely change dramatically.
Good luck, and this is by no means a stupid question ;)