Does the Bible indicate when the Ark of the Covenant officially disappeared? As the title asks, does the Bible indicate when, where, or how the ark of the covenant finally disappeared? 

If not, do we have any likely clues?
No, the Bible does not. This is the last mention of the ark in the Old Testament:

2 Chronicles 35:3


  And said unto the Levites that taught all Israel, which were holy unto
  the LORD, Put the holy ark in the house which Solomon the son of David
  king of Israel did build; it shall not be a burden upon your
  shoulders: serve now the LORD your God, and his people Israel,


After that, it fades from sight for the rest of the Bible until the apostle John sees a vision of an ark in Heaven in the last book of the Bible:

Revelation 11:19


  And the temple of God was opened in heaven, and there was seen in his
  temple the ark of his testament: and there were lightnings, and
  voices, and thunderings, and an earthquake, and great hail.


How it got there, or if it is the same ark, we don't know.