no, cookie settings are default. Same behaviour in ie, ff, and opera.
I think I figured it out though... in cPanel I have the domain forwarding directly to the shop's folder... and it wasn't matching the domain set up in configure.php
In other words... the htaccess file was forwarding domain.com to domain.com/shop while the site was expecting https://www.domain.com/shop
I changed it and it didn't seem to make an immediate difference (cookies catching up?) but now my problem seems to be gone.
I'm not sure if that makes sense or not... but I didn't change anything else.