Operation Failed when sending Email

Recently we converted a group of our users to offline cache mode in Outlook.  We are using Outlook 2010 on laptops with Exchange.

We have been plagued with 'Operation Failed' messages when trying to send mail.  No pattern. Only happens sometimes, and it does not matter if it is an internal or external email address.  The users are frustrated.

What we have tried:
1.) Deleting the address(es) from the users AutoComplete list and then manually re-typing the address in the "to" field.  That always solves the immediate need... but days or weeks later that same address may again kick up the 'Operation Failed' message suddenly.
2.) Clearing the entrire AutoComplete list from Outlook options.  Again, works short term, but the Operation Failed message eventually returns without warning.  Some users have dumped this list multiple times.
3.) Extending the setting for 'automatically save items that have not been sent after this many minutes:' from a default of 3 minutes to 20 minutes.
4.) deleting and recreating the users mailbox from the local computer and rbuilding the .ost file.

In all cases, the 'Operation Failed' message eventually returns...

What else can we try?  We have very frustrated users.  Most frustrating to them is when the Operation Failed messages occurs on a mail message with multiple recipients (sometimes 10-20 recipients.) because it cannot be easily determined which address in the auto-complete list is causing the failure.