Are you losing the complete emitter or just the top?

If you are losing the entire emitter. It should have dirt or rock packed tightly around it.

If you are losing just the top. I have fixed the problem by using 1" Pan Head screws. These are screws that have a large head on them. Pre-drill a small hole through the PVC and the emitters top approx 1" below the top of the PVC and through the cap. Make sure that the screws are long enough to go through both the PVC and the cap.

To show the approx location to drill and install the screws I have included a pic with a red dot. Install three screws evenly spaced around the emitter to form a triangle. If you try this. Make sure to mark the locations of the springs that keep the emitter closed if it has more than one to keep the screws from interfering with its operation. Bury the emitters top level with the ground.

Thanks for the tip and the picture. I was thinking of doing something like that but was hoping not to have to dig up the PVC. Looks like I'll have to bit the bullet. Currently, there's just a 4" hole but the grass around it hides it well.

Do you think there's enough water left in the French drain ( approximately 70') that mosquitos could breed? That's the only reason I would want it covered to be honest.