There are a multiple reasons for why an Outlook client can receive the 0x8004010f sync error. Unfortunately, 0x8004010f is just a generic MAPI error and will show up for a variety of problems.

Here is what the error looks like under err.exe (Microsoft Exchange Server Error Code Look-up Tool):

C:\WXP\system32>err 0x8004010f
# for hex 0x8004010f / decimal -2147221233
ecNotFound                                       ec.h
ecAttachNotFound                                 ec.h
ecUnknownRecip                                   ec.h
ecPropNotExistent                                ec.h
MAPI_E_NOT_FOUND                           mapicode.h
# 5 matches found for "0x8004010f"

This is what the error looks like from the sync log from within Outlook:

12:45:53 Synchronizing Mailbox <dgoldman>
12:45:53 Done
12:45:54 Microsoft Exchange offline address book
12:45:54 0x8004010f

Some of the most common reasons for Outlook clients to receive the 0x8004010f error with regards to downloading the OAB are listed below. Most of these are documented and I have linked articles to each of these to help everybody out. Please note that these solutions can change a small bit depending on unknown factors in a company's environment.

1. An administrator decommissioned the last Exchange server in a site and never pushes replicas to another Exchange server.
2. A new OAB is created in the active directory and the information store never reads the active directory during its maintenance schedule. This will result in the OAB files never being generated and the Outlook client will fail to download anything.
3. The information store has an invalid EntryID that points to the legacy EX:/ folders. Again there is nothing for the client to download.
4. An outlook client logging in from one domain to another domain and attempting to log in to another users mailbox.
5. The OAB was never generated or some OAB folders are missing from the public folder store.
6. Multiple OAB Version folders exist of the same type.
7. Clients are attempting to download the OAB files from a public folder store that have not received the replicated updates.
8. The offline address book list object has a missing address list. 
9. The offline address book list object has an incorrect address list.
10. Send/As changes in the store affect users accounts with no mailbox full rights to another mailbox:
11. Exchange 2007: The Client Access Tab on the properties of the mailbox store does not have an Offline Address List associated with it.

If you are seeing this error on an Exchange 2007 server and your OAB is generated by an Exchange 2007 server, please make sure of the following:

1. Make sure that you have added the replicas of OAB to the Exchange 2007 server

2. Make sure public folder replication is working.

3. Make sure the OAB is public folder enabled and you have OAB Version 2, OAB Version 3 and OAB Version 4 checked off so your legacy clients can download the OAB files from the public folder store.

4. Make sure that if you are using an Outlook 2007 client, your OAB is Web Distribution enabled and the OAB files have been replicated over to the Client Access Server. For more information on this process please see this blog:

http://blogs.msdn.com/dgoldman/archive/2006/10/23/outlook-client-fails-to-download-the-oab-with-error-0x8004011b.aspx and
http://blogs.msdn.com/dgoldman/archive/2006/08/25/How-Exchange-2007-OAB-Files-are-replicated-to-a-Client-Access-Server-for-download.aspx

5. If you are removing your last Exchange 2003 server from the org, please make sure that you follow our documentation on this process.

Dave