.....asks me for my password again and again and again.....
This is a hint but not aquestion.

First pay attention to:
http://b2evolution.net/man/2004/06/16/support_faq

If the problem exists furthermore, edit the file "_advanced.php" in the directory "conf".
Edit the line:
$cookie_domain = ($basehost == 'your_host') ? '' : '.'. $basehost;
'your_host' should meet YOUR configuration.
Examples:
'localhost'
'www.my_provider.com'

Have fun with logging in only once ;-)
Eugen