Hi John,
As far as I am aware all CA glues cure very hard and brittle. My understanding is that the moisture in the air/materials causes the glue to polymerise, forming a solid block of acrylic resin almost instantly. The thinner the glue, the better it will make contact with the surfaces being glued. Once cured, you have a thin block of plastic that fills the gap between the surfaces, causing them to stick together. However, distortion of those surfaces can cause the bond between the surface and the plastic to fail. Further stress will crack the cured glue.
The only way I can see any flexibility would be to incorporate a flexible filler, but that would significantly weaken the joint, as with the thicker CA glue derivatives which are never as strong as pure CA, since the bond structure is broken up by the fillers.
Loctite do have such a derivative which incorporates rubber particles and provides a flexible bond.
My preference is for PU glues, which aren't brittle, and have the added benefit of being waterproof.