I.E. which player would need the longest stretch of poor form (say consecutive matches with a high score of 30 for a batsman, or consecutive tests taking no more than 2 or 3 wickets for a bowler, or for a keeper a stretch of making few runs and consistently missing chances) before they would be dropped by their country? I am generally thinking in tests but you can do ODIs as well.
My top 3 in no particular order:
Chris Gayle - decent captain and no-one else wants the job, also WI have a dearth of quality batsman to potentially replace him.
MS Dhoni - good skipper and a massive star, I think he would get a lot of leeway with a bad run.
Kevin Pietersen - England's only world class player who has a reputation for either scoring big or not scoring much at all (last two years, 10 centuries to 5 fifties), so I think the selectors would keep the faith with him for a long time.