In other words, this smaller piece and the peach on white warp vs the white wedding present and the pale blue alternate, on which the knots stayed knotted as you would expect.
The first thing I did was to have the client of the wedding present contact the bride to warn her of the possibly demise of the knots at the end of fringes. Embarrassing but necessary, I thought.
Then I withdrew the pale blue piece from the gallery, and to my relief there was nothing wrong with the knots. The big difference was, the pale blue piece, (and presumably the wedding present,) had severely (?) twisted fringes, while the small and the peach pieces had looser fringes. (I've been trying to make my fringes less tight/wiry to harmonize more with the body of the cloth.) That little bit of difference, a few more rotations, seems to generate enough friction to hold the knots together.
And that concludes my fringing rush for now. Thank goodness, I was getting sick of it. Next I have three pieces and one fabric swatch of the old-fashioned wool. Fingers crossed, at this rate I can finish the unfinished jobs before I go. It's been hot and not nice to work with mohair, and I've been neglecting everything else. You should see the floor; no, wait; don't. Because as soon as I finish work stuff, I'm going outside. Pronto.