Natural peanut butter can remain unrefrigerated for up to a month without going bad.
If you want to keep the natural peanut butter fresher and help the natural peanut butter last longer than a month then you should refrigerate it.
When you refrigerate the natural peanut butter the natural peanut butter will last for up to 6 months before it gets stale.
The natural peanut butter would be safe to eat after 6 months in the refrigerator but it loses it's freshness and doesn't have as good of a texture or taste as it did before.
So if you're gonna eat the natural peanut butter within a month then it's okay to leave it sitting out at room temperature but if you're not eating the peanut butter up within a month then you should refrigerate it so that it will stay fresher longer and last longer.