Moodle allows faculty to modify test taking attributes for individual students.
Allowing a student to Retake a Quiz Activity
Go to your exam, and click on the Settings gear -> "User overrides"
Click "Add user override"
Search for the student's name who needs to retake the exam.
You may need to modify the "Close the quiz" time and date, if the quiz is closed.
Next to "Attempts allowed" change, the drop down to "2".
Click save near the bottom of the window.