Same thing here except there's no need to change the style; the contextual links do not show up no matter the style.
Were either of you able to resolve this on your own? I am encountering the same issue outlined by hass.
In my case, I needed to switch to the style "system block" in order to pull classes from the blocktheme module. This worked, but now the contextual link is gone. With the contextual link gone, it will be more difficult for the client to quickly edit the block's copy.
I wasn't able to resolve this. For the time being, I just put in some simple inline edit links at the end of my block that only show up if the user has access; checked with user_access().
I'm having the same issue.
+1 for this
This looks like a duplicate of https://drupal.org/node/1047392
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