Just stumbled upon a chemistry note that said dissolved gas in a solution will wreak havoc on a pH meter. If your Buffer will stabilize but not your sample then dissolved CO2 in your wine could be your problem.
If the Buffer won't stabilize then you probably have a bad probe, low battery, or a probe that is in need of cleaning (doubtful if this is a new meter unless they tried to repackage a faulty meter and sell it as new one)