When the "close" UI action is clicked, the following error is thrown "The selected parent incident loops back to this record"
Jakarta Patch 10
The issue is caused due to a parent loop
This issue is most likely caused due to a parent loop.
Say there are two incidents X and Y.
The issue occurs in the scenario when X's parent is Y and Y's parent is X.
When trying to close any of those two incidents, an OOB business rule named "Prevent Recursion of Parent Incident" that checks for the loop and aborts the action that is made on the either of the incidents.
To resolve the issue, please review the parent relationship of these two incident records and remove the one that is not necessary.