I have had what I call "carrion flies" (probably phorid -sp? - flies) as a problem. They look like fruit flies, but eat meat. So far, they only ever attacked dead or punctured eggs. The only real problem was when the babies began to hatch. Because they may take a few days to completely hatch, and the maggots only take a couple of days to reproduce, they can infest the hatchlings that take too long. I have had them get into the umbilical scar and eat out the insides of the babies. The best control I have found so far is to use an ultraviolet bug killer nearby, otherwise keeping the eggs in complete darkness. The bugs that I have dealt with are attracted to the light. Also, if you keep the eggs on the dry side, it helps. The bugs breed better with more moisture. Keep the eggs just damp enough to prevent denting.
Be careful about removing dead eggs. You can sometimes carefully twist them back and forth many times and they will come loose. But if they stick, I just leave them.