Tried to reproduce this with Drupal 7.34 and Panels 7.x-3.4. I created a page, selected In-Place editor for Renderer under General tab of the Panels edit page, added some blocks and added a Mini panel with blocks in it, went to the page and all the gear icons work. Maybe some JS issue is causing this?
Based on checks, I think Contextual links displays the edit link for the "renderer" only. Ex. if Blocks is displaying the Mini-panel, the contextual link module displays the "Configure block" link. Same for Panels with mini-panels rendered inside it. So that's the explanation why the "Edit mini-panel" link isn't displayed under the "gear" icon.
NOTE: Please correct me if I'm wrong with this analogy though because this is just based on observation
Solution 1: Using the Custom Contextual Links. Though this uses Tokens it doesn't get the mini-panel's name so if you had 10 mini-panels you should create 10 CCLs also w/c would be quite tedious though but of course if it's needed, nothing is tedious I guess? :)
Solution 2: Creating a custom module that would check each rendered "block" in a page is a mini-panel and if it is, display both the "renderer's" link and add the mini-panels link.