Warning, nerd alert...
This thread piqued my curiosity about metal alloys used in modern ski construction. I am a mechanical/aerospace/biomedical engineer, so I would like to think I understand the structural aspects a little. Modern skis are laminated composite structures (beams) typically with layers of plastic at the top and bottom (base and topsheet), fiber-reinforced composites (fiberglass, carbon fiber, maybe kevlar) and/or metal next, with wood or foam cores, all bonded together with resin/glue.
The way I see it, skis bend because the metal layers yield (undergo plastic deformation). I guess you could bend a ski without metal, but I think that would be a case where some components were cracking or de-bonding. I think the carbon, glass and wood components are not ductile enough to bend, but would crack (fracture) instead of yield. So, the most important material property of the metal that determines when a ski will bend (and stay bent) is the yield strength. To actually break the metal you have to exceed the ultimate tensile strength. Different alloys of aluminum have very similar stiffness, but can have very different yield and ultimate tensile strengths. Thin layers will have lowers stresses in pure bending, but if they are at the outer layer of a composite beam they will see mostly tensile stress. Thicker layers would be stronger in tension. I have seen layer thicknesses of 0.5-1.2 mm quoted in ski specs. A thicker layer should make for a stiffer ski that is less likely to yield in tension. I have not studied dynamics too much, so I don't have a good feel for why skis with more metal might feel more heavily damped compared to all carbon layups.
It was interesting to look at the Titanal link markojp posted. I always thought Titanal was a titanium-aluminum alloy, but it is in fact a 7000-series aluminum (which includes no titanium). Similar alloys are used in aerospace applications and bike frames. I don't know what types of metal were used in older skis, but I am guessing it might have been 6061 aluminum. Titanal has a yield strength about twice as high as 6061 (http://www.amag.at/fileadmin/AMAG/AMAG/Pictures_NEW/AluReport/AR_3_09_EN_Sports.pdf). AMAG also claims better adhesion for Titanal due to a porous anodized coating.
So, I think newer skis probably bend less frequently because they are using stronger materials, better design, and better manufacturing processes.