Who would guess it would be too hot to grow chile peppers? Mine are looking really peaked right now. They are burning up.
At my house, we take vegetable plants out when the produce starts tasting funny (bitter, whatever). Many not-so-pretty plants will still produce sometimes to an amazing extent. Diseased plants are another matter. It would depend on whether or not it is something that might infect the rest of the garden. Plants will grow long past what we expect if we put them to bed at night (cover them) when you start getting freeze warnings. Otherwise, I'd wait and see. I've had plants survive a few days of snow (I am in central Texas so we don't get much of this) and produce into the next year. It really depends on exposure. My husband heavily mulches everything in sight.