Once you open sauerkraut it should keep for up to 6 months to 7 months or a bit longer in the refrigerator as long as you keep it properly sealed.
When not using the sauerkraut always keep the jar sealed and then place it in the refrigerator if you're not using within a few hours.
If it's a can of sauerkraut you can wrap some saran wrap or other plastic wrap over and around the top of the can and secure it with a rubber band.
Homemade Sauerkraut should easily last up to 7 months in the refrigerator as well as long as you keep it properly sealed.
If you leave the sauerkraut out longer than a few hours then it could start growing bad bacteria and mold which could make you sick.
But just keep the sauerkraut refrigerated and it will be good for at least 6 months or sometimes longer.