Exchange 2010 Export Mailbox
Solution 1:
Well, I found this. It may be an option. Try running the powershell as administrator then running the command. This is apparently a known issue
http://social.technet.microsoft.com/Forums/en-US/exchange2010/thread/886a6c39-b975-408a-827c-fb3c07ea579b
Solution 2:
Step 1: Grant Full Access Rights
New-ManagementRoleAssignment –Role "Mailbox Import Export" –User Administrator
Step 2: Create a Network Share to save Exported PST files.
Grant Exchange Trusted Subsystem group read/write permission
Step 3: Run New-MailboxExportReuqest
New-MailboxExportRequest -Mailbox EricSimson -FilePath "\\SERVER01\PSTFileShare\EricSimson_Recovered.pst"
You can check the status of active export jobs with Get-MailboxExportRequest command.
More detailed steps are available here.