OWA 2000 can not be reachable via IE sometimes.

Some of the users can not access OWA 2000 via IE 6.0 and IE 7.0. Same users can access via Firefox without problems. The issue occurs not all the time but sometimes. When the user tries to connect to Exchange Server via Internet Explorer(6,0 or 7.0) OWA with necesarry credentialdomain\username) it is accepted after entering it 3 or 4 times. Then when the user clicks some folders in mailbox the password is being asked again and then the session is being closed(authentication fails)

The issue is same(owa does not work) until i logon to OWA with a user account which does not have any problem. If i logon to OWA with that user name and logoff and try to relogon with the user which have problems it works. After approx. 1 hour it stops to work again.

To make it more clear let me explain this way

User A: No problem with OWA at all. Works with IE 6.0, IE 7.0, Firefox.
User B: Has problems with OWA only with IE 6.0, IE 7.0. Firefox works without problems.

User A tries to logon to OWA, it doesn't work. Then User B tries to logon to OWA, works and loggs off. User A tries again to OWA, it works. It works like that around 1 hour and then again problem occurs.  

Issue happens on any workstation. The users are the members of same groups in domain.  Hotfix KB911829 is installed on exchange server.