Auto focus while using video

I use a Nikkor AF-S 18-105mm zoom lens with my D5200.

When shooting in video mode, the camera/lens combo won't auto focus.
It's fine if the lens is set to at 18mm, but if I zoom I lose focus.
Even though the camera dial is set to auto and the lens is switched to 'A', I have to use the manual focus lens ring.
Is there a setting I don't know about or is the D5200 incapable of auto-focusing zooms?

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Thanks

i am not sure that it will stay in focus while zooming. How does it do once you finish zooming? Does it refocus then or do you have to press the shutter button down half way to force it to focus?