Why does this lens lose focus when you zoom in but not when you zoom out?

This is regarding the Sony 18-105 E-mount constant-aperture zoom.

I took at photo at 18mm, focusing manually:

I then zoomed to 105mm, and took another photo, keeping the same focus:

Notice that the shot is badly focused.

This problem doesn't happen if you start with a 108mm photo, focusing manually:

And then zoom out all the way:

Why is focus lost when you zoom in but not when you zoom out? Is this lens varifocal only when zooming in, and parfocal when zooming out?

I read the theory that you can see better if you focus when you are zoomed in, but this camera has a 9.6x focus assist function, which lets you see what you're focusing.

Besides, cropping the original photo (the first in this post) gives a better result:

than zooming in (the second in this post). Why is this happening? If my focus was indeed off in the first photo, cropping it and examining the photo at greater magnification should reveal the mis-focus. But the original photo seems to be perfectly focused.

The conclusion seems to be that this lens is varifocal only when zooming in. Is this conclusion correct?

All these shots are with manual focus, F8, ISO 200, aperture priority mode, with a 2-second timer to avoid shake. This is on the Sony NEX-5R.

Answer

The lens is not parfocal in either direction.

What you have discovered is the difference between narrow Depth of Field (DoF) at longer focal lengths and deeper Depth of Field at wider focal lengths. The focusing error you introduce when you focus at 18mm and then zoom to 105mm is greater than the shallow DoF at 105mm even at f/8, so you notice how out of focus the photo is. The focusing error you introduce when you focus at 105mm and then zoom to 18mm is well within the DoF at 18mm and f/8 because the focusing distance is much greater than the hyperfocal distance for 18mm @ f/8.