Symptoms

An article is published in the KB. Someone will go in, click edit and make changes to the KB. The changes the article back to review status whereby the KB approve is unable to re-publish the KB. It is stuck in review status and grey out

Resolution

This behavior is due to a custom business rule. This business rule is setting the workflow back to review. The current out of box workflows being used are not designed for the workflow to move back to review from published. This is why the approval process is not firing. In an out of box instance, when a record is edited, it stays published and does not move back to reviewed. If you would like to keep this implementation, the workflows would have to be customized to send back out the approval process. 

If you were to disable this business rule, this would likely work the same as an out of box instance. An article only moves to Retired or pending retirement from Published. The article will remain in the published state after it is edited. If you would like an approval process to take place after a change is made a customization would be needed. 

The other possibility would be to enable the article versioning feature. Any time a published article is edited, a new version of the record is created. This new version would then go through the approval process (if approval publish workflow is set) and the original version would then be set to retired. 

Additional Information

Article versioning 
https://docs.servicenow.com/bundle/kingston-servicenow-platform/page/product/knowledge-management/concept/article-versioning.html