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Kitty has learned how to use the Pet Door, but still cries to be let in or out, from time to time.
That could be a signal your Kitty wants some attention from you.
When Kitty cries to be let in or out, ALWAYS, pop open the Pet Door to judge his reaction.
If he refuses to go out, then pick him up and give him affection, but do not open the big door.
If he refuses to come in by the Pet Door, peak out to make certain he isn't hurt or unable to use the door. Then pop open the Pet Door and encourage him to use it. When he is inside, give him praise and affection for using the door.
I stress this again, don't use corrective measures if your cat doesn't use the Pet Door. Positive re-inforcement is a much better means for this type of behavior modification.