Whipping cream that has been frozen won’t whip

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As Alton describes. As you beat the cream bubbles of air get worked into the mixture. The beating makes the bubbles smaller and smaller until the fat globules touch and the mixture becomes stable.

As you mentioned- if you whip it a little more then the fat will coalesce and squeeze out all the water and air and you have butter.

Time is a factor in this process (when done mechanically) in that it is required for homogeneously sized and distributed bubbles. The fats have to stay plastic.

The fact that it can be done very quickly is easily seen with whipped cream chargers. The gas is pressurized into the cream- upon release expands into the tiny bubbles we need.
How does a whipped cream charger work?

The brands that used to work may have changed their formulation in response to carageenan shortages. If they use less emulsifier, a lower quality product, or different emulsifiers such as guar gum, locust bean, or xanthan gum, the stability of the whipped cream may suffer. If the cream you can get isn't stable enough, you can add unflavored gelatin to stabilize it. Method is in 'Joy of Cooking', or here.

May2013: Looks like carrageenan is still on the USDA organic list Shortage has eased, but whipping problems could still be due to variations in quality of supply.