[Sans Peur]

The shifting is done by 2 solenoids on the transmission. It could either be the reverse solenoid is going bad (most likely) or not receiving power from the shifter on the dash.
Go below and put a meter on the solenoid wire and have someone shift the lever into reverse. If it is getting power it is the solenoid. You can also swap the connectors between the forward and reverse solenoids. If it still won't go into reverse (when you shift the lever into forward because you reversed the wires) then it is the solenoid. If it goes into reverse and not forward. Then it is the lever.