Rub the solid brass object with steel wool and a paint stripper to remove the old protective acrylic coating and any dirt. The steel wool and paint stripper is sold at most hardware stores.
Choose a fine quality brass polish such as Simichrome metal polish, sold at most hardware stores. Another ideal metal polisher is Flitz Liquid Metal Polish.
Pour some polish on a clean dry rag -- a cloth diaper works well. Rub the polish into the brass until it lusters and shines.
Protect the brass from the elements by applying a new finish -- a non-abrasive, polymer-based car wax, sold at automotive shops. Apply the wax to the brass with a dry clean cloth just as you would wax a car -- around the surface of the item in circles.
Maintain the protective sealant for longer periods by applying several applications of the wax coating.