Larry - We see the construction of the Ark of the Covenant as clearly described in
Exodus 25:10-22 (KJV). With the extremely low mid-east humidity and the fact that it was overlaid with solid gold, rot and decay of the wooden elements would have been very slow - if at all.
It was not only protected from weather by the guilding as it was carried in the migrations by the Levites, but it had the hand of God upon it at all times to protect it. We know this from the incident where Uzzah had a bit of an issue with touching the Ark as told in
2 Samuel 6:3-7 (KJV).
Sometime between the days of King David, around 1000 BC and about the time that Josiah became king in 628 B.C., the Ark had vanished. We know this because Josiah sought to restore the House of the Lord and asked Levites to bring forth the Ark. The Levites said they were “unable to comply.”
Perhaps we should just ask Harrison Ford and George Lucas of Lucasfilm, Inc., as to where they placed "it" after they finished making their 1981 movie...