We are using EO Web dialog control in our application, Our license covers the entire EO Web suite.
After implementing this in our application and deploying it in the stage environment which is having https configured , its throwing mixed content warning , below is the root cause we have analysed

Its the java script which gets added while rendering the page

<script type="text/javascript">
//<![CDATA[
if (!window._eo_js && window._eo_autoInit && window.confirm("EO.Web Controls Client Side Debug Message:\r\n\r\nThe control library wasn't able to automatically initialize correctly. Please refer to http://www.essentialobjects.com/Go.aspx?id=1002 for instructions on how to intialize EO.Web controls manually.\r\n\r\nSelect OK to redirect to the above page automatically."))window.location.href="http://www.essentialobjects.com/Go.aspx?id=1002";
//]]>
</script>

Let us know if you have any resolution for this

We don't get security warning frequently for our HTTPS site, but sometimes we do get that warning our observation are as below

1. Security warning pop's up when page has message box call through JavaScript.
2. Basically if page is under processing (i.e. server is in progress for the request) and in between that JavaScript function which has message box at that time we get this warning.
3. If that EO Web message box is replaced with alert then we are not getting this problem.
4. We get this only for HTTPS site.
5. Trust level is full for our project and for High our site is giving configuration error.

Security Warning Popup says, "Do you want to view webpage content that was delivered securely?"