Cannot edit path of shape containing an image, once already edited once before.

I've got a rectangle with an image inside it. I was able to select the path to move one of the anchor points, making the rectangle into a slightly different shape. I would now like to edit the path of that shape again slightly, but I cannot — there is no way to select the path. Clicking on the border of the shape as I did previously produces no results. How can I edit this path?