I had the exact same problem. I loved my stocking holders but they would slip off easily even before Santa came to fill them. And then came the news stories about children pulling them off on their head! That is scary!
So, I did this about 8 years ago and it has worked like a charm ever since. I put tiny, tiny nails in the back of my mantel, by the back wall. (I suppose command strip hooks could work too!) Then I took fishing twine (the clear kind) and looped around the stocking holders (at a good solid niche) and anchored it on to the nail. Initially, it was tedious getting the twine just right but now I just pack away the fishing twine with the stocking holder and hook it right on each year. I put green garland over the top and no one ever sees it. I actually keep the tiny nails up all year round and they aren't visible. I feel so much better about my kids being near the fireplace knowing there is no way they are going to yank down those stocking holders! Plus Santa's loot can't weigh them down either.
Hope you find something that works for you!