This was happening to me a few weeks ago when I started using a "new" computer for my primary internet work; the symptoms were almost identical. I had composed a letter to this worthy column, but since it was also happening to a few other auto login sites, there had to be some other factor unique to my (new) system.
Eventually I traced it to a setting in my security suite (CA) which was (apparently) default programmed to remove cookies immediately upon use (it's well disguised under the Privacy settings). I removed the tick from the box and the problem disappeared.
It seem likely that a similar little helpful "feature" in your machine/software combination may be responsible in the same way. Persist, hang in there. There has to be an answer somewhere
. After all we are working with the new unknown here - computers and software - much more complicated than flying!
Regards,
FOR