If a car is reaffirmed do further payments on the car have to be reported to CRAs by the lender after discharge or is the account closed permanently?

If you sign a reaff on the loan, then it keeps going under the old loan except for any new provisions of the reaff... so yes, all payments should be recorded.

Note though: Some Buy here/Pay here places work like other debts (Mainly medical bills) and do not report the "good" (timely payments), only the "bad" (missed or late payments).