some bitch's coats can and do go dull during a season, and some loose coat ( i'm assuming this is what you mean by brittle, coat should'nt be breaking as such) during a season, but some can loose coat,( if that makes sence). it will pick up after season has finished, but can take time.
i'm not a great believer in supplimenting , as complete dogs food should have everything a dog needs in it, as for the food, what food suits one dog, does'nt mean it suits all dogs.