I am suffering from the same problem. I simply went into social integration and disabled stumbleupon button. Then I went to the stumbleupon forum in the link above and made a new complaint. Perhaps if you and others do the same they will finally look into the issue.
CH (Official Rep) replied to this problem:
Share buttons won't work in SSL environment
We have no immediate plans to support this issue with relation to Https:// - sorry about that.
Looks as if those of us that run in a https environment will just have to disable StumbleUpon sharing. Really sad as I liked being able to share via SU.