Sorry for the delay.
Can you tell us more? Is this Outlook connected to an Exchange Server? If so I would first ask the server tech person about this.
If not, tell us what you mean by 'it usually closes'. What does, Outlook or the message? Is your Preview Pane enabled? If so, when you delete a message or arrow down, does the next message display in the preview pane then disappear?
If the next email 'closes', what happens when you highlight that email in the list?
Does AVG scan your emails? If so, can you disable that as a test?
I use Windows 7 Pro x64 and Outlook 2010. until recently, when I delete a message or click the arrow to move to the next message, then next message opened. Now, it usually closes. I have set and reset the option "open the next item: in: File>Options>Mail>Other>After moving or deleting an open item:
The only thing that has changed on the system is I upgraded from AVG 9 to AVG 2012.