Polishing the sign with a very mild compound may remove some of the staining. I'd probably do it by hand, the paint on these signs is pretty thin, I'd be concerned about buffing thru. Although using a small buffer on low speed would probably be ok, just a risk of going through on the edges and corners especially.

I don't know of a way of preventing rust other than keeping the sign in a dry environment. Waxing the sign may help I suppose.

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