Firstly it should be noted that there is a dispute whether there were two Aronos- one for war and one which resides in the sanctuary, or whether it was the same Aron which only once was taken to war. The latter view is that of Rabbanan in Yerushalmi Shkalim 3:1 and according to them your question is not relevant. According to Rabbi Yehuda Ben Lakish who argues with them, we find this Aron in the desert but it is unclear whether it was used afterwards. According to Tosafos (Eruvin 63b D'H Kol) there was only one Aron in the Beis Hamikdash and the other Aron was not in use after the time of David Hamelech (presumably it was dismantled or hidden), whereas others maintains that there was another Aron in the Beis Hamikdash, which may have been maintained by the Levites (see Sifrei Naso which calls the Levites camp "the camp of the Aron" and some commentators explain that this refers to the second Aron which was kept in their camp in the desert and was on Temple Mount but not in the sanctuary. (Rabbi Dovid Fardo, Safrei Dvei Rav).

It would appear that this Aron did not have Kruvim like the other one and only contained the broken tablets. It is likely that it was hidden like the other one but at a much earlier date.

Yoel Domb