Logs with debug mode :

Started GET "/hosts/auto_complete_search?search=" for 192.168.200.117 at Mon Jul 23 11:16:35 +0200 2012
Processing by HostsController#auto_complete_search as JSON
Parameters: {"search"=>""}
Setting Load (0.5ms) SELECT `settings`.* FROM `settings` WHERE `settings`.`name` = 'authorize_login_delegation' ORDER BY LOWER LIMIT 1
CACHE (0.0ms) SELECT `settings`.* FROM `settings` WHERE `settings`.`name` = 'authorize_login_delegation' ORDER BY LOWER LIMIT 1
Completed 401 Unauthorized in 123ms

You need to setup apache with REMOTE_USER header (authentication delegation).

To be clear : the websso is working : I'm authenticated with
authorize_login_delegation and Foreman find my user.
However the only thing is when I clear my browser cache,
I get asked just once at the precise instant when I click on
search tab with a HTTP authentication window (not /users/login).

In the log I get a 401 Unauthorized if I don't log myself