I've fished with bead chain swivels for years and never had one break. I use them on my Silver Horde plugs and have caught many a large chinook with no failure. I do prefer good ball bearing swivels for most fishing but have never experienced what you show in your picture. I would probably re-tie as if one broke just pulling your knot tight then you might have got a bad batch. I know there's been more than once in my life where I thought "gee I should probably re-tie or fix that" only to not do it and then lose a nice fish shortly thereafter and kick myself all the way home.