I had a great deal of trouble with eye contact for a long time in therapy, but I did outside of therapy with everyone else as well. I think sometimes for shy folks it is just too much self-exposure. You're being stripped down and showing your soul. It takes time to build trust. Gradually, little by little, my eye contact improved. By the time of my last session, I'd completely lost all fear of looking him in the eyes. And I found that to be very freeing for me. I was completely comfortable being myself. A huge gain for me and one that I've taken with me since I've left therapy. But he never ever forced me to look at him...or even brought it up for that matter.

I would say do only what you feel comfortable with doing and in time, as you gain trust, everything will likely fall in place for you. You'll find yourself looking more when you feel ready to.