The most likely cause is an electrical contact/communication problem between the lens and camera. Since autofocus works with the Kenko teleconverter inserted, the TC may be changing the physical contact pressure/alignment enough to restore the connection, or it may be reporting different lens data to the camera instead of simply passing the lens ID through.

A good first step is to inspect and clean the lens and camera mount contacts carefully, and make sure the spring-loaded contacts on the lens move freely. On Nikon F-mount, those spring contacts are on the lens side, so a sticky or dirty pin can cause intermittent communication.

If cleaning the contacts does not help, the issue could be a deeper internal connection fault in the lens itself rather than the camera body. In short: the teleconverter is probably masking a lens communication problem, not fixing autofocus in any normal way.