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ABCT doesn’t necessarily account for the length and severity of the Great Depression. That was largely fueled by multiple factors of intervention in the economy. For a good Austrian source on this, see America’s Great Depression (as well as the links included).
As for “preventing” depressions, the best method is zero intervention. Let the market function. But on that note, could you please provide your source for “Hayek’s definition of inflation”?
Either way, the only argument for growing the money supply is the fearmongering argument against “deflation”…but this has been debunked. There is no legitimate reason to purposfully inflate the money supply with the specific goal of “stabilizing prices” or any other sort of centralized planning end.
For resources on deflation:
Why Deflation Isn’t Harmful by Jörg Guido Hülsmann
Also, here’s an abridged version of Prof. Salerno’s assessment using a specific case, and his full paper is “An Austrian Taxonomy of Deflation” (PDF) and there’s also
An Austrian Taxonomy of Deflation—With Applications to the U.S. [PDF]
Also see here for a list of threads on the topic, and then of course there’s the Mises Wiki.