Mine shafts on earth are limited in how deep they can go by 2 things, internal heat and rock pressure. The deepest mine on earth currently is just under 4 kilometers. There is internal heat on the moon caused by tidal pressures, but it is very deep. The motion core is a tiny portion of the whole compared to the earth. With 1/7th G gravity, I wonder how deep you could go before rock pressure got higher than the compressive strength of the rock? I'm guessing pretty far. My question is; how deep could a lunar mine go before heat or rock pressure made it impractical?
I came here with the same question. While rock pressure is one issue, I think the limiting factor is actually heat.
The most recent paper I could find on Lunar temperature gradients is Nimmo 2012, which gives a gradient of 2.5C/km starting from 30C near the surface. As the deepest mine on Earth is apparently limited by a temperature of 66C, it follows that the deepest 'traditional' mine on the Moon should be ~14km.
That Wikipedia article is sourced from Wired's 2012 article Digging for Riches in the World’s Deepest Gold Mine.
That said, the highest temperature borehole I could find on Earth is 355C, and again it follows that the deepest borehole on the Moon should be ~130km.