How can I stop mortar plugs from popping out of slab holes?
If you do it your self (not endorsing, and see comment by The Evil Greebo) you could put a more secure plug in by using hydraulic cement. 

To ensure that it does not come out, holes or cracks are usually back cut (the hole is made wider below the opening so that its diameter is greater than the diameter of the opening). This can be done with a small masonry chisel and a small sledge hammer. Start chiseling about 1/2 to 1 inch below the opening and go down about 3/4 to 1 inch deep.  You just need to get it a bit wider (1/4 inch greater all around) than the hole.

The hydraulic cement is used like a putty and it expands slightly as it dries to lock it in.  Follow the instructions, especially about moistening. 

If you are doing this yourself, use a good mask and gloves because there have been harsh chemicals in that hole. Let the chips and dust fall in the hole. Do not vacuum them out!