Recording is a bear, and there are a lot of things about it that can take you out of your center.
I remember something Chuck wrote in a thread last year; that 90% of a producer's work is done before the session starts. I'd say the same goes for the musicians. Beyond being prepared musically, there's a whole host of things about your attitude, desires, and expectations that need to be addressed going in. You have to cultivate a LOT of self-acceptance. You have to trust your instincts, and trust the people you are working with. I usually have no problem staying in the moment, in fact those moments seem quite heightened. Although it could be said that in recording, everybody has a tendancy to think more about the product than the process, which may be another way of not being in the moment. Staying relaxed is difficult. One thing that sometimes works for me is to focus on the spaces surrounding my phrases, rather than on the phrases themselves. Just make sure there's space in there, and the rest might just take care of itself.
Welcome to the forum, Jason!