There are actually a whole lot of scenarios in which this could happen as there are various features in Outlook which allows you to automatically delete emails.
There are also some scenarios in which emails directly get deleted outside the control of Outlook.
Message Rules in Outlook
This is where to start your investigation. If you’ve created rules to automatically delete messages when they meet certain conditions, it could be that such a rule also applied to a message you did not initially expect it to apply to.
In this situation it is recommended to verify your “delete” or “move to Deleted Items folder” rules or to disable them for the time being to find out if that was the culprit.
Web mail (serer) rules
As in Outlook, most mail servers also allow you to create rules via Web Mail. In that case, the processing takes place at server level so they can still be processed when Outlook is closed.
This is particularly handy for IMAP accounts so messages get sorted on other devices as well, such as a smartphone or tablet, which often do not support message rules. Another scenario is to prevent Junk E-mail from being downloaded.
Junk E-mail Filter with option to delete immediately
The Junk E-mail Filter in Outlook can also be the culprit when you’ve enabled the option: Permanently delete suspected junk e-mail instead of moving it to the Junk E-mail folder.
While for most people the Junk E-mail Filter doesn’t filter out real email (false-positives) with its setting to “Low”, it can never be guaranteed that it is 100% accurate. Especially when you have your filter set to “High”, it is better to leave this option disabled.
When you really only want to receive emails from your Safe Lists, then this option might be useful.
3rd party Virus scanners and Junk E-mail Filters
Just like Outlook’s own Junk E-mail Filter, ones that you’ve installed yourself (or via a Security Suite), could cause the same result.
Verify their settings or disable these add-ins for the time being to find out if they are indeed the cause. In the case of a virus scanner, it is recommended to disable its integration with Outlook anyway.
Another feature in Outlook 2010 and Outlook 2013 is: Ignore Conversation.
This feature is intended to stop emails from a specific conversation of which you are a recipient to end up in your mailbox and directly deletes it for you. For instance, when everybody constantly uses the Reply All button and the conversation stopped being meaningful to you at some point.
It will still be available to you then in the Deleted Items folder and that is also where you can undo the Ignore action. Simply click on any message in the conversation and press the Ignore button again. The entire conversation will then be moved back into the Inbox.
A similar feature like Ignore Conversation is: Move Conversation.
Rather than just deleting the conversation, it will always move messages belonging to that conversation to a specific folder instead. When you selected this to be the Deleted Items folder, then you’d still achieve the same results.
To undo this, right click on any message from the conversation and choose: Disable Always Move Conversation.
Smartphones, tablets and other devices
Yet another reason for messages to get deleted as soon as they are being received is because they are being moved or deleted automatically on another device.
This can be due to (spam) filtering but also because you are using IMAP on some devices and POP3 on others but did not enable the POP3 option to leave a copy on the server.
Finding out whether this is the case is quite easy; Completely turn off these devices or remove that email account from the device. If email arrives properly in Outlook now, you know that Outlook isn’t causing it.
When messages that you expected don’t arrive…
When you’ve checked all of the above and messages that you expected to arrive still don’t arrive at all, there are still some more things that you could check. For some steps, you may require some additional help from the original sender to verify where exactly the message gets lost.
When messages disappear after a few seconds…
When your messages don’t disappear directly but still only stay in your mailbox for a short period of time before they seem to dissolve.