Then you should use cross-domain cookies in setcookie() function. In Joomla!1.6 it can be changed in global settings, but in Joomla!1.5 it requires few patches:
1. In libraries/joomla/application/application.php replace (here domain.com is name of your 2nd-level domain; note dot before the name):
setcookie( JUtility::getHash('JLOGIN_REMEMBER'), $rcookie, $lifetime, '/' );
by
setcookie( JUtility::getHash('JLOGIN_REMEMBER'), $rcookie, $lifetime, '/', '.domain.com' );
and
setcookie( JUtility::getHash('JLOGIN_REMEMBER'), false, time() - 86400, '/' );
by
setcookie( JUtility::getHash('JLOGIN_REMEMBER'), false, time() - 86400, '/', '.domain.com' );
2. In libraries/joomla/session/session.php replace:
setcookie(session_name(), '', time()-42000, '/');
by
setcookie(session_name(), '', time()-42000, '/', '.domain.com');
