To make a change to a process (workflow) in CRM you need to be logged in as the owner of the process. If you are not the owner and you try to make a change, you get the following error: The Process cannot be published or unpublished by someone who is not its owner.
To remedy this, select the process, click the assign button and change the owner to you. Now you can update and activate / deactivate the process. When you're done, you can reassign it back or keep ownership, whatever makes more sense.
TECHNICAL NOTE: This same principle applies during import of a solution, if the solution has an updated version of a workflow in it, the person importing the solution must be the owner of the workflow in the CRM system or it will fail.