What will make a Chevy Cavalier's blinker lights and back up lights go out even when you change the fuse?

I don't completely understand the question, but as I do, you are asking why the lights do not work even after you have replaced the fuse. A common denominator is the ground system in the back of the vehicle. We are assuming that this car hasn't been in a wreck whereas the fuse keeps blowing because of a short somewhere. Take a test light and connect it to the negative side of the battery (negative ground)then probe the leads at the lights and see if the test light comes on. If it does, then you need te try and determine where the ground wire problem is, or if it was me, I would just attach another wire somewhere on the chassis and connect it to the common ground wire for the rear lights.