The version of Microsoft Exchange you are running, and the particular client the user is using to access public folders (Outlook 2000/2003, Outlook Web Access, IMAP4, etc.), have an impact on these problems. I'm going to assume you are running Exchange Server 2003 and Outlook 2003.
Public folder permissions are complex. Since you verified that the folder permissions are correct, I think it could be an information store permission problem, rather than a directory or client permissions (a.k.a. folder rights) problem.
Compare the permissions on the two servers where the public folder replicas are homed at the file system level. By default, authenticated users should have permissions to the actual database files. If the permission has been removed or changed, that could create an access problem for your user if he/she is not a member of a security group that has access.
The public folder store is in %systemroot%\program files\exchsrvr\mdbdata\pub1.edb and pub1.stm by default.
Speaking of defaults, also check the default public store setting on the user's mailbox store. This setting is actually what dictates which public folder server the Outlook client will connect to first.
In the event that the replica is not on that server, Outlook will receive a referral list of replicas from that server. Connector costs, blocked referrals and manual referral lists can all affect how a user gets to a replica and could be related to your user's problem.
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A similar issue has happened on a few sites here. Some computers would have the issue, others would not. It was cured by checking the RPC services on the client and adding the following statements:
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