Can anyone explain to me how property values go down, yet property taxes go up?

Right. Property taxes are based on valuation as per the tax assessor. Remember though that the assessor looks at property value completely different than the average market home buyer. Taxes are assessed based on the valuation of land and any improvements (houses/buildings, landscaping, and utilities/services) placed on the land. Market buyers base their valuation on supply versus demand, and area market rates. In an appreciating market this works out well for the home owner, because taxes generally don't raise very much annually, and real estate appreciation will on average grow at about a 5% to 10% annual growth. Unfortunately you are currently living a depreciating market in your area, so your market value is lowering, but the property remains the same in the assessors eyes.

Get your home re-assessed if this is the case... This is unusual, if you give me your address I can pull a title report and see what the county has for your assessed value. Perhaps the city/county you live in is upgrading the enviroment and added the additional property tax recently?

Appeal your assessment. The valuation can't increase if the fair market value is truly going down.