wp-admin redirects to wp-login and throws me out

Hi -

Really frustrating problem here... wonder if anyone can help?

I've just restored a WP/BuddyPress site to a new URL at http://www.getambition.com. It all works fine. I can login, and it directs me back to the homepage, and shows me as logged in.

However, whenever I try to access WP Dashboard by gong to wp-admin, the site logs me out and redirects to /wp-login.php?redirect_to=http%3A%2F%2Fgetambition.com%2Fwp-admin%2F&reauth=1.

This wasn't a problem on the dev site. Any ideas what might be going on? I've changed all the references to the site URL as far as I know, and all other aspects of the migrated site are working just fine. However, I can't access the Dashboard at all.