There is a permission to allow "Edit". But, then that allows the role to edit every post.
Is there a way to allow users to permanently be able to edit their own posts?
Yes, you can set this in dashboard/settings/posting. A little further down on the page is Discussion & Comment Editing, change this to Authors may always edit.
My goodness. I don't know how I looked over this multiple times. I apologize for even asking this when it was right in front of me!