Theme doesn’t keep homepage settings

I have the home page set to the page called Home, and the blog page set to the page called Blog (sometimes in trying to make this stick I choose a page called Articles).

The home page settings will look sort of as they should in the customizer, but while the slider is on, it isn’t showing, and the category I choose for the fashion category doesn’t display either. Very strange behaviour.

The page I need help with: [log in to see the link]