Hello Randy,
Do you have a non-Yamaha sustain pedal plugged in by any chance? The DX7 is setup to work with the supplied sustain pedal. If a different manufacturer's pedal is used, it could cause exactly what you describe.
If you do not have a pedal plugged in at all, try selecting a patch that has the infinite sustain. Enter EDIT MODE, and then go to all 6 operator's EG rate 4 parameters and set them to 99. Then go to all 6 operators EG level 4 parameter and set them all to 0.
If this doesn't give you a note off after letting go of the key, i would think it's time for a service center visit.
Andrew