All right, I made another login page first that isn't SSL, then I added CAPTCHA to login pages (under admin > user settings). CAPTCHA works on the non-SSL login page as it should. CAPTCHA does not work on the SSL login page, same as with the SSL contact page.

Adoucette - unfortunately, this problem with Captcha is a core issue rather than something which is being caused by the Feedback Module.
I traced it through the code and can tell you how to resolve it but it does require a recompile of the URLRewrite module.
If you think you can do this, then here are the steps:

a) Open up URLRewriteModule.vb (located under DNN455\Library\HttpModules\UrlRewrite) - I believe there is a project reference already to this if you open up your DNN 455 solution.

b) Scroll down to Line 348 where it reads If strURL <> "" Then

c) Change this line to the following
   If strURL.ToLower.Contains("captcha.aspx") Then
         'Don't do anything since this is a captcha URL
   ElseIf strURL.ToLower.StartsWith("https://") Then
        ' redirect to secure connection
        Response.Redirect(strURL, True)

The rest of the block should be left as is. That is to say the main change made is that you check for captcha first and then check whether the url starts with "https://"

I have tried this with my copy of 4.5.5 and it is working as expected. I am sure the core is aware of this too and will probably be fixed in the next release as it becomes available.

Once you've made these changes, remember to recompile.