The explanation in the Apocrypha was that Jeremiah hid the Ark in a cave in Mt. Nebo before the Babylonian invasion, and that its location would not be revealed until God was ready for it to be found. It was never found again and was absent in the Second Temple. The Nebo theory finds support in the apocryphal book of 2 Maccabees. The narrative in that book says, "the prophet, warned by an oracle, gave orders for the tabernacle and the ark to go with him when he set out for the mountain which Moses had climbed to survey God's heritage. On his arrival, Jeremiah found a cave-dwelling, into which he brought the tabernacle, the ark, and the altar of incense, afterwards blocking up the entrance" (
2 Maccabees 2:4-5).
The late Ron Wyatt caused a stir back in 1982 claiming that he had found it in a cave near Jerusalem and developed a stunning story about how the blood of Christ dripped through the creavices in the rocks and fell upon the mercy seat of the hidden Ark.
Only problem is that his location was wrong according to my information. Jesus was crucified "outside the camp" - near the southern summit of the Mount of Olives. "Outside the camp" is defined as being anything over a radius of 2,000 cubits (or 3,000 feet) from the door of the Holy Place in the Temple. So criminals, like Jesus, had to be executed over this minimum distance from the Temple. So his findings do not mesh with the known Jewish law of Jesus' day.
http://www.arkdiscovery.com/index2.htm