Not only can you freeze them yourself, you can purchase them already frozen. Egg Beaters - one brand of egg "substitute" - are, after all, essentially nothing but egg whites, and you can freeze egg whites with very little problem.

The various companies that produce these substitutes say that you can keep them in the freezer for a year without sacrificing quality. Thaw them in the refrigerator for 12 hours or longer. Once thawed, use them up within a week.