Update: My disappearing cookies are for Chase Bank and FTM, but there may be others that I've never run into. The other sites with which I had a problem turned out to be victims of cache clearing.
I've now emailed Cookie's dev 3 times and not received a response - I guess it's a selfish reaction to my having called him out...story upon request.
At any rate, I've now trashed Cookie. (I guess I'll give it another try after a looong hiatus.)