For me, I can't keep eye contact with a guy that I am into. I get really nervous. He always complains and say that I am not paying him any attention so I just straight up tell him that I am nervous. I'm pretty sure she is just nervousness if she is willing to go on a second date with you. Just tell her to relax. Do humor or something to get her out of her shell. :)
like the people have said below it is all down to nerves or she finds it hard to stare into your eyes. I find it off putting if people avoid eye contact, but seeing as its a date I put my money on being nervous as it is very common. Next time should be easier as she should be more relaxed.