We mill the dowels to extremely tight tolerances and then press-fit them into the loom frame. Inkle looms operate under very high tension and stress may elongate the holes. Or if you store the loom in very low humidity, the dowels may shrink.
If dowels become loose, you can glue them into their holes. Use common woodworker’s glue (aliphatic glue) such as any of the TiteBond glues, Super Glue (cyanoacrylate), or epoxy glues. Spread a thin and even layer of glue on the inside of hole and press the dowel back in until the shoulder of the dowel is pressed firmly against the frame.
Do not apply glue to the dowel, and do not use too much, or you'll get a messy squeeze-out of glue. If you get squeeze-out with an aliphatic glue, wipe it away with a damp towel before the glue dries. If it's too late, or you used a different type of glue, wait until the glue dries and cures. Then use a sharp woodworking chisel or razor blade to remove the excess.