Why did the inverse correlation of stocks and commodities stopped working in 2008?
The problem in your question is the "and vice versa".

To give a very simplistic view, the problem in the 2008 crisis was not on production side - companies had enough to produce, but no-one to sell to. Given this, excess commodities found no buyers, even as the price lowers. The inverse correlation of stocks and commodities supposes full capital use, which is not the case during the 2008 crisis.

Globally, the correlation between commodities and other stocks is around 0, though during full capital use periods it does tend to be negative, there is usually a positive correlation during crisis.