Willi,
Do you have a solid spar along both the leading edge and the trailling edge? If you've just got hardware store dowels laced together, I seriously doubt it'll stay together. If you're just using thread, or run of the mill twine, I'd suggest you switch to waxed cord. Once you knot it, it doesn't slip, and it's really pretty grippy (plus, it's authentic, the Wrights used it extensively).
Have you done any research on how Chanute built his glider?
This link looks like a pretty promising start. I highly suggest writing to the NASM archives as well. They say they are willing to answer 1 letter from an individual per month, and I write 1 letter a month, because they are incredibly helpful. (If only they translated L'Aerophile...)
This isn't to discourage you, you've made way more progress on this than I have on pretty much all of my projects. Good Luck!