The analogy is flawed on many levels. A more biblical analogy would acknowledge that you're already dead when the Coast Guard gets there. Lu 9:60 Ro 6:13; 2Co 5:14,15 Eph 2:1,5,6; 5:14; Col 2:13. You couldn't grab the rope, because you're dead. In fact, you've been dead for days, and you stink. That's the analogy the Bible gives us in the story of Lazarus.
The biblical view is that Christ truly saves you from out of death. He regenerates you to life. The biblical teaching is that we were dead; completely unable to respond to God (Ro 8:7). Unable to see with dead eyes. Unable to hear with dead ears. Dead ears cannot hear. Lazarus could not have heard Jesus' voice when he was called out of the tomb unless God made Lazarus' ears work. Lazarus did not "grab a rope." God revived a dead man and restored all his faculties for him to respond and to come out of that tomb. The Biblical view is that we can truly thank God for saving us. He really did it. He didn't just provide a potential salvation for those smart enough to "grab the rope." He really saved us out of death, made us alive. He didn't just save us from dying. We died. He revived us. I can truly say "Jesus saved me." The Open Theist can only say, at best, "Thanks for the assistance."
The Open View teaches that men are their own Saviors. It is a works salvation. It is a self-absorbed, self-gloryifying, self-aggrandizing theology that exalts man and denigrates God (Job 40:8). The Open Theist worships the creature instead of the Creator (Ro 1:25), deifying Man to be His Own Savior, and humanizing god to be only a little higher than the angels (if that). The Open Theist wants the final word. And that's the bottom line: What good is Jesus' sacrifice? If it depends on you, then it's not sufficient. Jesus doesn't save. You do. It takes determination, tenacity, a strong-will to grab and hang on to that rope. Jesus' sacrifice doesn't save anyone. It's just a rope. A rope doesn't save.
What's the difference between the guy who doesn't take the rope and the one who does? The one who does is smarter, better, more reasonable, more thoughtful, more glorified. He has something to be proud of, a badge to wear on his chest, flowing robes, and trumpet to blast. "Great job, Open Theist! Way to go, man! You did it! You grabbed the rope! It's all you, baby! Sure, the rope was there, but what good is the rope if you don't grab it, right? You da man. You. Da. Man!!!" What about Jesus? Oh, Him? He's just a Rope.