It sounds in your case like the authorization was designed to go to the nonssl server for admin. If your admin/includes/configure.php set both the ssl and nonssl servers to '
https://mydomain/ then I doubt you would have the problem. If your authentication uses one of the built in osCommerce functions to go to the admin index then try adding ,'SSL' to the arguments in the file as in:
tep_href_link('gohere','parameters'); defaults to a non-SSL connection
tep_href_link('gohere','parameters','SSL'); links using the SSL connection defined in configure.php
AARGH! I just found out what was causing my problem. GoLive changed the code on the html web form from action="" to action=(Empty Reference!) when I copied the signin file from our test site to the working server. I think I'm going to have to see if I can find a preference in GoLive to prevent it from updating links when importing files. Sorry to bother everyone here.