The Customizer Home Page Slider (WP Admin > Appearance > Customize, Theme Settings > Home Page) doesn't appear to be passing data to the customizer. Adjusting the Home Page Slider doesn't allow you to save the customizer and when you change an unrelated theme setting in addition to the slider, changes to the slider aren't saved.
The code that monitors changes to the slider widget can be found here. This code hasn't been changed in a long time so this issue was likely introduced after a semi-recent SiteOrigin Widgets Bundle update or WordPress update.