When going to a secure page or link/site... the https with a padlock symbol flashes briefly in the browser bar then vanishes.
Can you please provide a specific URL where this happens? Most often, this means that a page has subresources that are served over plain HTTP, so the page as a whole is not loaded securely.
On regular Safari and other browsers like FireFox and Chrome... show the padlock on secure pages. Just try it here with https://bugs.webkit.org browser will flash the https and padlock and then it vanishes.
It think it might have been resolved since long and we didn't have any reproductions steps and it was never confirmed. Marking this as 'RESOLVED WONTFIX'.