This does not seem to be right. Once the blog post got published by a moderator, the contributor can update it on his own without further moderation.
I tested it with the contributor test user and was unable to reproduce the behaviour described here.
Once the post is published the user should see an update button only, that is a publishing activity with saving the changes.
Can you provide a step by step reproducible example with screenshots about your published blog post and what buttons you see in the publish widget?