Hi Martin,
I had a look at your site. There is a JavaScript error coming from your custom dark-slide code. The script starts with (function () {, but the closing })(); is missing. The browser therefore reports SyntaxError: Unexpected end of input.
I also noticed that the desktop Site Title currently links to /category/work/, not to the front page. That category is empty and does not have the Fullscreen Slider enabled. The mobile Site Title, on the other hand, links to the actual front page.
In Lay Theme itself, clicking a link that points to the currently active page is prevented and does not destroy or reinitialize the Fullscreen Slider. So at the moment it does not look like the slider is being toggled by Lay Theme’s same-page handling.
Your reload workaround is currently active, so I cannot reproduce the original behaviour directly. With the workaround enabled, I clicked the Site Title several times and the slider stayed active.
Could you first fix or remove the incomplete dark-slide script and make sure both the desktop and mobile Site Title link to the actual front page?
Then temporarily remove the reload workaround and test it again. If it still happens after that, let me know and I’ll take another look.