Sauerkraut can keep for several months if it is stored in an airtight container and stored at or below 36°F (15°C). Refrigeration not required, but it greatly increases the shelf life of the Sauerkraut. Many commerical producers also use pasteurization to further increase its shelf life.
http://www.germanfoodguide.com/sauerkraut.cfm
It like a pickle

After opening a glass jar of sauerkraut, how long does it stay good? It has been kept in the fridge, of course. I'm not sure since it is fermented, I would think a couple weeks.