Yes, this is a correct procedure. I think even 1 leg without the problem does suffice. I've seen enough operators with a HIL list full of the same problem opened and closed again. This has always puzzled me why it is not better regulated. Just hope your company has a good engineering department that picks this up, and takes action.
You can also push the mechanic to put in the book something like "due to ungoing problem, item transferred to HIL with original due date".
