Should my property value appraisal go down due to flood zone?

I live in Fayette County, Texas. FEMA recently re-drew the flood zone map, and my property is in it. Because my home is financed, the Mortgage Company requires me to carry Flood Insurance, resulting in an additional cost of almost $ 800 per year. Homes in my area that are not in “THE ZONE” do not have this added expense. Based on this info, shouldn’t this drop the value of the property, thus dropping my property taxes??? Should I decide to protest this appraisal, would you please provide me with some insite on how to go about presenting “my side of the story”, and perhaps some tax law and/or property appraisal info that I can reference to back me up?

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