The Bible does indicate that the earth will always be mankind's home and it will never be destroyed. (Psalm 104:5; Psalm 37:29, 115:16).
There are several clues in the scriptures which help us to see that we will not have repeating cycles of history with mankind falling into sin and corruption and needing to be restored.
For one thing, the Bible indicates that Jesus only needed to die once, for all mankind, forever. (Hebrews 7:27, 28) The value of his sacrifice is completely satisfactory forever, because his perfect human life corresponded to Adam's. (1 Timothy 2:6; 1 Corinthians 15:45) That ransom gives God the legal right to forgive repentant sinners and restore them to perfection without breaking his own standard of justice. (Deuteronomy 19:21). Once the value of this ransom has been fully applied to mankind, and those living have regained the sinless and endless life that Adam gave up, any future offspring would be born without any inherited sin or death. (Romans 5:12; Revelation 21:4)
Another line of evidence is that Satan and his demons will be completely destroyed after the final test at the end of Christ's thousand year reign. Prior to this they are only restrained, so that they can be "released from his prison" to see who will still choose to follow them even after attaining perfection. After that final test Satan and all who choose to follow his course of rebellion against God are completely destroyed in the "lake of fire". (Revelation 20:2, 7-10) Fire is here used to represent destruction (which is what fire does). Burning there "forever and ever" indicates that their destruction is permanent, as in they will never receive a resurrection. After the rebels are destroyed, those remaining will have already been tested and proven to be faithful. It is unlikely that a person would choose to rebel after that, but if they did, they could simply be destroyed quickly without dragging the rest of us down. This is because any future rebellion by any individual person could be handled totally differently from the initial rebellion of Satan, Adam, and Eve. At that time it made more sense for God to allow them to choose an independent course in order for humans and spirits to see that such a course can never work for them and their offspring. Certainly by the end of the final test, God's universal sovereignty, or his right and ability to rule will have been fully proven to the satisfaction of all reasonable humans and spirit creatures. (Jeremiah 10:23; Psalm 34:8)
Another way we know our problems are being handled in a permanent way is because of God's qualities such as love, holiness, wisdom, and power. His love makes him want to end suffering forever. (1 John 4:8) His holiness makes him incapable of allowing wickedness to exist forever. (Isaiah 6:3) His wisdom and power make him capable of knowing and achieving the best and permanent solution. (Daniel 2:19)
This is what Jehovah's Witnesses believe. For more information visit jw.org