I placed some lanterns against the wall on the outside of the wall. My companion refuses to walk past them and just stands there staring at it and doesn't move anywhere again, no matter where I go in the building and how many times I say "follow me". Once I removed them the issue went away.
I want to add to this that companions seem to love standing on any fire they can find. They really should path around fire so they're not constantly burning when I'm home.
Same issue here on Offline mode.
I have a small base with one door, the companion would often follow inside no problem, but now that I've placed a crude wall lamp outside next to the door the companion never enters the building.