Здравствуйте Furic, Вы писали:

F>My ISAPI filter receives request, sets session ID to cookie,
F>runs some routine to authenticate client and return to IE SF_STATUS_REQ_FINISHED_KEEP_CONN.

This retcode does not guarantee that connection will be keeped.

F>After client presses REFRESH, ISAPI should check authentication result for this session ID.
F>But what happens is the next:
F>when i go to the server like http://localhost/MySecuredPage it works fine
F>but when i go http://www.mySiteName.com/MySecuredPage , get page with cookie and press "REFRESH" i get "connection to server couldn't be estableshed. Connection closed".
F>What is the problem ? does IIS behave different for this situations ?

Please, describe the problem in more details. Show the cookie attributes (the best way is to show a response header here). And what browser are you using?