You may no longer be able to write further messages (items) to the Outlook or Exchange mailbox.
It could be for various reasons.
Mostly likely out your are of disk space, or size of Outlook or Exchange mailbox is too large for the set limits. Size limits are usually 20GB for Outlook 2003, 2007, 2010 etc. Limits can be modified see http://support.microsoft.com/kb/832925. Just under 2GB for Outlook 2002 and below.
It could also be that the PST 'Disabling the AutoArchive and Personal Folder File' feature is turned on in the registry. You can see http://support.microsoft.com/default.aspx?scid=kb;en-us;Q258277 for details. HKEY_LOCAL_MACHINE\Software\Microsoft\Office\[REPLACE_WITH_OUTLOOK_VERSION]\Outlook\
Set DisablePST to 0 for not disabled
It could also be due to other security issues writing files.
New Outlook PST size limits are mentioned here: http://support.microsoft.com/kb/982577.