I will try to explain what is going on and why is it happening, it took me a while to figure it out.
I've only seen this once in another case about 2 years ago, and I suggested using a different menu (which doesn't use element cloning) instead as it is impossible to properly solve this. I still highly suggest a different approach, as element cloning really narrows the possibilities of placing other than simple elements into the header.
This time I took some time to figure out something that might solve this, although I cannot guarantee it will work properly each and every time. Place this script code into the footer of your site, just before the closing body tag (footer.php file in your theme directory, or equivalent):
This is a really fishy solution, I honestly cannot guarantee it's going to work properly, but it's worth a try.Best,
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