The WP Stealth Note message window appears all the time on my site, even though it's supposed to only appear once every 3 days.

Please make sure that you don't have any "caching" plugins on your site (like "W3 Total Cache" or "WP Super Cache"). If you do, deactivate them, or at least disable their caching option.

Obviously our plugin isn't compatible with HTML caching, because it generates different content depending on visitor's cookies, while the caching plugin captures the page content when it's accessed for the first time and then serves the copy of content captured instead of dynamically executing the code of WordPress and the plugins on your site.

Caching plugins can be useful when you basically want to show the exact same content for everyone who visits your site all the time. But they can cause issues when the content has to behave dynamically.