Hi Ann,
You really shouldn't have any problems saving and storing cosmos seeds.I'm assuming you are waiting until they are completely mature before picking. So I'm a bit baffled. Cosmos seed just needs to be kept cool, dark, and dry so nothing out of the ordinary. They normally germinate quite well in the spring. I did have a bit of a WSing problem with them this year as in many sprouted and then there was a frost. Most of them died. All my other WSed sprouts lived, so they must be very temperature sensitive. So make sure there is no chance of frost when sowing or use containers outside and bring them in if a frost is coming then transplant them once it is warmer.
The only other thing I can think of is not all the seeds are fertile. Maybe you are not getting good insect pollination on them or it is just a varietal thing. If I were you I would save way more seeds than you actually need then over sow in the spring so you are ensuring some will sprout.
Remy

I'm finding that either soaking them before sowing (better), or keepting the soil pretty damp (which gives other problems later), helps germination a lot.

Seems like the seed coats on some cosmos are harder, and they'll start to sprout and get "stuck" and die. Pre-soaking might be the help those kinds need. I haven't read anything about this, but I had better results with this experimental soak. (1-2 hours or even try overnight)