Natural Peanut Butter can remain out of the refrigerator at room temperature without the need to refrigerate it even when it's been opened.
If you do want to refrigerate the opened natural peanut butter then you should stir it up before refrigerating it.
The refrigerator will keep the natural peanut butter fresher longer but there's no requirement to refrigerate the natural peanut butter even after opening.
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.