I have a 455 John deere mower. When I pull the pto switch the blades engage. But as I keep mowing the blades kick off and on. Put new pto switch in. put new battery on. Voltage from alternator is good. Could it be the pto solenoid? If not then what?

That would be what I checked out next.you might check the wires and connectors make sure all is tight and not broken.

Check reverse safety switch, at back of mower on right side of mower free wheeingl lever