Absolute nonsense to claim verse 13 refers to the physical life when verse 12 is clearly referring to a declension in the spiritual life. Does it not say that Godly "agape" love will wax cold as the world gets worse? Only the saints can be recipients of agape, yet Jesus says the agape of some of the saints is gonna grow cold and dead!
Therefore, since verse 13 is in the same context of verse 12, the message of Jesus is that some of the saints are gonna die spiritually and those that endure to the end the temptation to join them in spiritual death shall be saved.
Why would Jesus supposedly concern us with preservation of physical life in the tribulation, as you suggest, when over and over He tells us our lives are but sheep to the slaughter, vapor here then gone, crucified all the day long? He ain't concerned about the physical in the least - He's got new bodies ready to go. What He is concerned with is our spiritual life, without which those new physical bodies mean nuthin.