Is there a way to set up a data partition so that a user cannot close a request?
Yes you can. You will need to create the following data partition constraint and assign the data partition to an access type or contact:
Table Name: Call_Req
Constraint Type: Update
Constraint: (status='ACK') OR (status='FIP') OR (status='FC') OR (status='PND') OR (status='PND_S') OR (status='RFA')
Note: The status codes listed above are the statuses that a user can set the status of a ticket to.