We need Nick Hoffman or another geologist's input...But I believe yes, it is still sinking.
The entire area is a delta region. It is formed out of river silt and sand that was deposited over tes of thousands of years (but it is still relatively "new" in geologic terms). With time, this "new ground" compresses, and thus "sinks" in elevation because it is not replentished with new silt and sand by Mississippi River flood waters. (the levies surrounding the city prevent the city lands from being flooded and the silt from being replentished).
The region probably has additional sinkage resulting from the removal of oil, simialar to what you've seen in your region.