I'm having the same problem. SS support were of no help.
The website footer also disappears.
I've tried everything: removing and re-adding all nav content, logos, different styles and configurations of header. Always reverts back to white when clicking 'Save'.
It's not code injection because I'm not using any. It's not custom CSS because I removed it all and it still happens. It's site-wide, not related to any specific page.
Even the footer I tried deleting and completely rebuilding and that doesn't help either.
Something has gone wrong in the backend with Squarespace to cause this and I hope they can find and fix it ASAP.