Discovered the solution to a problem which happened on a previously functional site, where repeated logins became required and the session information no longer appeared to transfer from non-secure server to shared secure server. It turned out that the time on the SSL shared server had become out of synch by one hour. Once the server times matched again, all problems disappeared.

If you have a similar set-up, one quick way to check for this problem is to use the Who's Online facility in Admin/Tools and track yourself within your catalog as you move from secure area to non-secure area, and back (e.g. from Catalog to My Account). Remember to refresh the Who's Online page in your browser to see the change. If you notice that the session for your IP address either disappears or the time changes significantly, it may indicate you have a similar time synchronization problem.

I spent many hours looking for solutions to session/login problems and so far didn't see any other reference to server time synchronization.

I hope this information may help others.