This is the number of attempts the application will make before it triggers the "If No Link Is Found" action. That is, if set at 3 (and the previous setting at 7 days), the application will make 3 attempts to look for the link (21 days) before it takes the "If No Link Is Found" action. You should leave this at 3 attempts  to ensure that the partners website was not simply experiencing unexpected downtime when the application was checking their website. You can imagine how irritated link partners would get if they are having hosting difficulties and then the "Link Management Assistant" starts informing them that it couldn't find your link. It would be the least of their worries.