If the tractor is less than 10-12 years old, chances are it's designed to shut off the blades when the transmission is put in reverse. Some John Deere and Honda tractors have an override where you can force the blades to engage when in reverse.
Very similar logic is used on walk-behind mowers with a blade brake clutch; the operator has to complete an intentional, 2-step procedure to get the blade to spin. I suspect this is the law-of-the-land, per the US Consumer Product Safety Commission.
Probably Step 1 is to find out if your tractor has a engage-blades-in-reverse feature. If it does, then you can start testing and troubleshooting to find out why its is not working.
Caveat: I work for Honda, but the preceding was my opinion alone.