If you want to solve it permanently, use T-nuts and machine screws. Remove microwave; insert machine screws in the holes, then thread a T-nut behind the face frame. Tighten it enough so that the T-nut starts to set in to the wood.
After all four nuts are set, reinstall microwave, and use the machine screws to tighten until the T-nuts are firmly pulled in to the back of the face frame. I painted the heads of the machine screws to match the black of my the microwave surround. That's optional.
In case your aren't familiar, a T Nut is a nut that has spikes that are set into the wood. Do this and it'll never loosen up again. You are basically "through-bolting" the screws.
To really make it robust, get some backing plywood cut into little squares, and glue them on the back of the face frame at each corner. Drill through the hole in the face frame through the piece of added backing wood. Then install the T-nut. This ensures there's lots of wood for the nut to set in to, without and risk of compromising the face frame.
Also, while you have the microwave out, install more sheet metal screws in the frame that holds the microwave to the face plate. They have a tendency to loosen up as well, so add more to strengthen that whole thing.