The Domain Mapping plugin, when activated, and a site has a domain mapped to it (www.site.com/site1 maps to site.site.com), clears out the screen for the Appearance > Customize. When clicking the Appearance > Customize section in the Admin page for the site, you get a blank page on the customization screen and you only see the widget on the left.
The bug exist on another domain mapping plugin, and there's a workaround for it. Wonder if we can incorporate the fix to this plugin: https://wordpress.org/support/topic/problems-with-theme-customiser-on-mapped-domain?replies=7
Please let me know if you need any further details.