Can a recruitment agency continue to approach candidates that they have recently placed with an employer and charged a placement fee for?
Yes, getting placed doesn't necessarily remove you from their contact list.
You can always respond and tell them that you're no longer looking for further placements and ask them not to contact you again.
You may need to repeat this request, as people may forget to remove you from the list (or only remove you from one of many lists/databases).
Unless there is a specific clause in their contract with the employer preventing such approaches then yes they can.
They generally don't though - not so much because of ethics but because it's a really low return. People who have recently placed are generally unlikely to want to change again so soon, unless of course they are really unhappy with the new role in which case it's not really the recruiter's fault if they choose to move on.