There is a teaching floating around in Christianity that speaks of "endurance" as part of the criteria for salvation. In other words, you only get saved if you "hold out to the end" in your belief and actions as a Christian. The thought being, that if you should ever "leave" your Christian beliefs, or if your actions get to a point that causes people to doubt your salvation, then you probably weren't saved in the first place. And our Daily Verse is one of those passages these "enduring Christians" use to defend their teaching.
One helpful thought for any of you who might be confused about this matter is that the word "saved" as it is used in the Bible speaks primarily of being delivered. That is what our salvation in Christ is: it is a deliverance from Satan's kingdom and an entrance into God's kingdom. Note Colossians 1:13, "He has delivered us from the power of darkness and conveyed us into the kingdom of the Son of His love." And it is deliverance that Jesus is speaking about in Matthew 24:13, deliverance from the trouble of the end times. God will rescue His own.
Please note that in John 10, the "Great Shepherd" passage that in verses 28 and 29 Jesus speaks of our being held in both His and His Father's hands. They are the ones holding us, not the other way round. Sure, we can "hold hands" with our Savior, but the "endurance" there is not how well we hold on, but how well God holds on! And Jesus made it very clear that God will never let go!