After opening peanut butter it can last up to 4 months in the refrigerator however I've always just left the peanut butter jar out on the counter because I use it often enough and it never has gone bad being opened up and left out on the counter.
You really don't have to refrigerate peanut butter unless you want too and it's supposed to keep the peanut butter fresher but it's okay to leave the peanut butter out of the refrigerator if you want too.