It seems the exchange server has a policy to delete any emails older than the "retention" day (say 60 days). When I open my Outlook 2010 client, old emails on my local also got deleted. Is there any way to restore these deleted emails? So that I can back them up first.
If you did not back them up before they were deleted then they are lost.
In the future archive your emails after 30-45 days to prevent this.
Contact your IT Support Staff for assistance they might be able to recover them from their own archives.