A little more information.
It seems that if I set a large linked script as the last script tag in the head of the html, this causes it more often than putting it above other script in the head of the html. I can refresh the page repeatedly and get the OnInitialized to not fire sometimes. If I put this linked script toward the top of the head, it appears to not occur as often, which would indicate a load timing issue.
One more updated... I added an alert to the IE Implementation CuteEditor_OnInitialized stub and in repeated refreshes, I would get that alert rather than my overridden alert in the html after the cute editor.