Lifetime cookies should scare the xxx out of affiliates. They are open to abuse and have been abused extensively back when they were common. They can put the majority of affs plain out of business.
As far as my preferred tracking goes, it is two week or one month overwriteable cookies. It can be argued that the last site finally convinced the player to sign, but the first site did the branding and that branding laid the ground work for the conversion. Branding installs trust and is way too underrated in this business.
Since IE also has tabs now, the described scenario is quite common I think. I use IE that way all the time.