Wife needs her husband's permission to go out if her going out contradicts with his rights as a husband and needs from her.
If the husband permitted her to go out and she thinks that the situation is same, then no need for repeated permission every time, as far as she knows that he will not object. This is called ITHN AL_FAHWA اذن الفحوى (Understood permission).
Recommended fast also needs husband permission if it contradicts with his rights as husband on his wife. If husband needs his wife for intimacy relationship during the day, she can not refuse him because of recommended fast.