Will the new heavens and new earth last forever?
Yes, the new heavens and new earth are eternal. The context declares God will create them for all eternity, and they shall remain before Him. This new creation comes after the destruction of the present universe and continues into the eternal state, where Israel also remains before God.
Les explains that this passage in Isaiah points to the same event as Revelation 21 and 22. He notes that even though the present heavens and earth will be destroyed, God will create new heavens and a new earth for all eternity. Isaiah records that they 'shall remain before me, saith the Lord.' Les says this occurs after the millennial reign and after the total destruction of the whole universe, not just the planet. In the eternal state, Israel will still hold a unique position as the apple of God's eye, and members of the body of Christ are in an even better position.
For as the new heavens and the new earth, which I will make, shall remain before me, saith the LORD, so shall your seed and your name remain.