Unless it's a logic board issue, and the pixels themselves aren't "dead", one dead pixel will not cause another one to die. Period.
Also, if anyone mentions the "just rub the dead pixel and it will come back to life" thing to you: it's bunk, it's possible to damage neighboring pixels, and it will almost undoubtedly scratch your screen. Perhaps, one time out of a hundred, with a particular cause of dead pixel, it works. Maybe. But it's a bad idea. Just mentioning that because all too often someone "helpfully" posts in with a recommendation to do that. I was leafing through an Apple service manual at Borders last night (oh, the fun that I have!) - mainly because I was amazed to see an Apple service manual at Borders - and it specifically mentioned the dead pixel rubbing "remedy" as useless and potentially destructive to the screen. It even informed the tech to look for scratch marks to determine if other pixels had been damaged by attempting this technique.