Green Card
I am sure a lot has changed since 9/11. However as far as I know with a green card you have to come to the states at least once a year. When I was in Saudi years ago there was a French National (Green Card holder) with an American wife. He didn't have any problems. My wife also know some folks from India who have a green card and visit once a year to keep it current if you will. They don't seem to have any problems at all. They have been doing this for the last 20 odd years.