When it happened to me it was a cam failure. One of the exhaust cam lobs just went away causing the exhaust valve to remain closed on that cylinder. The engine started running rough and kept getting rougher. I screwed around for longer than I care to admit before I started for a place to land, I also lost about 500 feet of altitude. In my case the engine never stopped running, the oil temp, oil pressure, the single cylinder head temp (not on the affected cylinder) and exhaust gas temp were all normal. As you may have guessed this is a subject near and dear to my heart!
There are lots of things that can cause an engine to run rough or quit, mag problem, improper mixture, bad fuel, carb ice, even an air filter collapsing and partially blocking the intake. There are only a few things we can do to try to fix an engine problem in the air. They are all on the engine failure checklist. If you haven't fixed your problem with that checklist your not going to fix it. Go someplace and land safely while the engine is still running and do not descend until you are over your landing area. Even at a controlled airport if you tell the tower you have an engine problem and don't want to descend until your directly over the airport he will help you get down safely. If the controller gives you a hard time declare an emergency. That is the gist of my debrief for the rough running engine exercise.
BTW, even it the pilot does everything correctly on the rough running engine exercise I usually give them an engine failure too. I'm just a SOB when it comes to emergency training.