Not being an attorney and with that being said I would think if you list the prior effective date on your search as well as the new effective date you would only be liable for the results between those two dates. 

  I always double check the previous search as well and have found errors which the client really appreciated that was found.

  It also can get a foot in the door with a new client and, in time, may get them to switch over to you for their original orders as well.