Node contextual links don't appear when block added to region via Context

I am unsure if this is an issue with Context, Node Block, or just my setup. When I add a block via the blocks page, I can see the node's edit/delete links in the block's drop down menu. When I add a block to a region via Context, this does not appear to work, and all I see is the configure block link. Is there some way to make this work?