An automatic transmission not going into reverse can be caused by either faulty transmission bands or other faulty components in the transmission or a transmission control solenoid.
A common cause of a transmission not going into reverse but going forward is due to a faulty transmission control solenoid.
Or the transmission bands could be bad or the transmission is about to go out and needs rebuilt.
Usually a transmission needs rebuilding if the transmission is not going into reverse because soon it may not go into forward gears.
I would take the vehicle to a transmission shop and have the transmission checked out and possibly changed out or rebuilt.