Generally I don't delete any work related emails or file them in folders.

I never know which messages I'll need for future reference, so I leave them all in the 'inbox'

Outlook seems to have some archiving feature, which will archive emails past a certain date. The only problem is I can't find them again. They seem to have disappeared.

Can anyone help?

In Outlook, go to File > Open > Outlook Data File. If you can see Archive.pst, select it and open it. Otherwise copy & paste the following line in the "File name" box:

%USERPROFILE%\Local Settings\Application Data\Microsoft\Outlook\Archive.pst

Good luck.