Political Stability and Economic Success

I think it's an influencing factor. And I also think it depends on the type of market.

I'd say it would be one of the major contributing factors. Ecnomic success would be hard to acheive if the political situation changes constantly from one extreme to the other. No one is going to invest large sums of money into building something up if they fear a new government is going to come into power and seize it from them - that goes for homes as well as factories.

Suppose there is a basic system stability (that is, no new government is going to do big anti-business changes, such as nationalizations), but there are still several levels or stability.

Let me put some examples:
China is politically stable, but still quite autocratic, and has had enormous economic success in the recent years.
Postwar Italy was politically unstable, but within the dominance of market economics, yet it was also a success story.
Yet sometimes, it seems that market economies suffer is there is too much political bickering, and not many agreements are found within the democratic party system.

Ah, so you are separating the obvious political instability that directly results in economic instability (e.g. nationalization, privatizing, pegging and unpegging etc) from just general political instability?

I'd agree, it represents an unknown and the market hates that.