Why do I keep getting rejected for credit applications?

I've had my first student credit card for about 6 months now. I always pay above minimum on the payments. I have a credit score above 700. But I keep getting rejected for credit applications. I am trying to build and establish credit so that in a few months I can buy a used car, but I am worried I won't be approved even with a co-signer. A year ago, my pport was stolen and I put an alert on my credit and my social security. I also have a pretty short credit history. Is this affecting my credit applications?