Mining costs are only indirectly related to the value of bitcoins.

When the value of bitcoins drops below the cost of mining, it makes no economic sense to mine. So people who mine for profit should stop mining. This means it will become cheaper to mine again, and there should be an equilibrium.

However, there are also people that mine for other reasons than economy, or who expect that the price of bitcoins will rise enough to get them out of the costs.

(replace bitcoins with gold, and you'll see what has been done in gold-based economies for thousands of years)