Saved Searches only save the criteria of the search however, we exclude the date and time as we allow this as manual input every time. Your designated support contact can log an enhancement request to have these fields added as part of the saved search.
One feature we are working on for 14s1 is the ability to go back to your last search results after looking at details of some of the items in the search results. This will only last until your run another search or do some completely different task e.g. create a new contract etc.
If you have any other questions please feel free to email me directly: firstname.lastname@example.org
Sr. Product Manager - Ariba Contracts