After splunging into the mysteries spreaded on the internet around the mirror Yata no Kagami I found out that the reason that it cannot be seen is that
there's something written on the back of which isn't entirely Japanese. Regarding the stories of some people like Yano Yutaro, a ex militairy officer it is written in Hebrew. When I stick this to the novel of this author Ben Midland I conclude that it explains what the Japanese government has to do with it.
They just don't want it to be observed, afraid of what might happen. As far as I concern, it will be the evidence of all the rumours on the Net about Jewish tribes reaching Japan in the late Yomon era.