Mirage was my very first Transformer. Good news is that this is not that one. The OG lives safely with my brother's collection. This one, on the other hand, decided to do a nose dive of the shelf a few years back. Finally got around to fixing him.
The peg that connected his waist snapped clean off.
I removed these two screws which separates the two halves of his waist/hips.
The break left a nice little divot perfectly centered in the bottom of the torso. First i used a push pin to make a little ding, centered in that divot. Then I took the point of an Exacto knife blade and spun it around in that ding to make a bigger pilot hole.
Than with a drill and a small bit, I honed out the hole. First by drilling the hole clean through, then rotating the figure around the spinning bit to hone it more. I kept doing this until I felt the hole was smaller than the screw, but big enough that the threads had some meat to dig into, but not stress and crack the plastic. I did the same on the hole in the torso so it could spin freely on the screw's threads.
I used a screw to replace the broken peg. This one was 3/4 in. long and the thread diameter was just bigger than the hole.
Using the pelvis half as a stop, I screwed the screw in until there was enough space to hold the to halves of the figure together, and left a little space so it wouldn't be too tight. Then reassembled him until he was whole again.
Whammo! Now he transforms just fine, and can get back in the action.