Derogatory phrase asserting that the subject is rapidly losing status, quality, morality, or generally going down the tubes.
Actually originates from Britain, referring to the practice of going to grayhound racing events (still held in a few places in Britain, there is a dog track in Walthamstow in north-east London), where people (almost exclusively men) bet on the races and drank alcohol.
Like most fun things it was condemned by the moral majority (see oxymoron) and hence is generally considered a bad thing.
Related interesting facts:
The artwork of the popular album Parklife by the band Blur is based on the Walthamstow dog track.
The techno anthem "Born Slippy" by Underworld is named after a grayhound, as is the superb breakbeat track "Pearl's Girl".