Do you have an example of this in mind where the known "tit for tat" strategy falls short?

I don't have a concrete example, but I think you can invent plenty of iterated prisoner's dilemmas with whatever modified rules and variables and find 'tit-for-tat' isn't the end-all-be-all. Like it changes things if there's an infinite or an unknown number of rounds, some of the defects are 'noise', etc.,.