Outlook sent emails disappeared

I've seen cases where a user somehow moves an email or folder into the calendar or contacts folders, which aren't displayed as folders in the normal outlook 2013 view.

Try searching, based on the subject or recipient, but set the scope to "All Outlook Items".  

Also, click the ". . . " button at the bottom of the outlook window, next to "Mail, Calendar, People, Tasks".  On the small menu that comes up, click Folders.  This will change the view to display the complete folder structure of the mailbox, including calendar, contacts, etc, similar to how previous versions of outlook displayed them.  This makes it easier to dig around and find items that have been misplaced.

You may also want to use the 'Recover Deleted Items' feature in Outlook. Depending on your Exchange organizations settings it could still be there if it was removed or deleted from a folder.

Sorry guys I forgot one piece of information. All the recipients did not receive the emails. I have a full view of the folders and had changed the scope to all Outlook items

Did they send the "lost" emails via an activesync device. I've seen that happen. Otherwise it sounds as if cache mode may be your issue as wirednet suggested.

Ok, have you checked the Drafts folder?  Maybe they started a reply, but never actually sent it?

(I realize that it should be found by search if it's in drafts, but if the emails weren't received, and the exchange server itself has no record of the messages, then the logical answer is it was never sent.  Either it should be in drafts, or they started a reply and neither saved nor sent it.)

tshearon - They sent the email from Outlook.
Steve Whitcher - The emails are not showing in OWA either

I have also tried Recover Deleted items in Drafts, Outbox and Sent Items but nothing is showing there. We have 30 days retention set.

Resigned to the fact that the emails probably just got lost.

While the accepted solution is technically valid, I would like to clarify that this can nevertheless be a real problem.  I have only been on 2013 for a few weeks, and have just experienced the same issue, and now need to go and figure out what replies have been lost, as I lost close to a day’s worth of replies.
My scenario is not un-similar to the above, but with a few tweaks.  I usually hibernate my laptop, go home and connect via the VPN, hibernate again and connect via the LAN when back at work.  I used to close Outlook and some other apps before hibernating, but recently got lazy and stopped doing this, and most time it would be OK.
At more or less the same time I experienced the problem, Outlook would go into “not responding mode” more and more often, and towards the end it was happening about every 30 seconds (e.g. it would happen twice while trying to type even a short sentence), making it impossible to work.  So I eventually restarted outlook (the main outlook windows closed OK, but the notification window and reminders window were taking forever, so I eventually forced them closed via task manager).  The foregoing may of course not be connected to the missing sent items, but the possibility is there, so I have included the info in case it helps other people.   Anyhow, after restarting outlook, both problems have been resolved, for now.
Yeah, it’s not a real explanation or solution (I suspect the hibernation and/or network switching may be triggers, but who knows), but if my experience resonates with others, maybe we can get a bit closer to cracking the problem.

And it has just happened again (well, last night actually).  This time I was on the LAN at work, I had reinstalled OFFICE 2013 to try and sort out a separate OUTLOOK issue, which in turn killed LYNC.  So last night before I left I tried to reinstall LYNC, which seemed to freeze at about 90% complete (in fact my whole PC froze, even the computer time display).  So I forced a shut down, BUT this could not really be the cause of the problem, as the lost e-mails should have been sent between 20 - 80 minutes earlier.  But, I did have a failed install of LYNC earlier in the day (stupid me did not think to close OUTLOOK before trying the re-install which I assume was the cause of that), but maybe that failed install unset Outlook for a while.

(Also LYNC actually did seem to install OK after all, as I was able to use it the next day).

I'm also experiencing other random issues with 2013 the most common one being that reminder and notification windows do not always close when I close Outlook, typically they have always been the last to close, but reasonably promptly, now I sometimes have to force them to close.