The first crisis occurred in the 1930s. Economists had no theory, at the time, to guide policy for addressing the dramatic drop in the volume of output and the increase in unemployment. John Maynard Keynes, as well as Michal Kalecki, developed the theory to address this crisis.
As I recall, the second crisis of economic theory relates to the mix of goods being produced, even when the volume is such that more-or-less full employment is being achieved. Many of her time did not think the balance correct. Conspicuous consumption, positional goods, and the means of destruction are produced in abundance. But as for the production of amenities useful for modern life typically provided by government (e.g., public transportation) - not so much. Mainstream economic theory does not provide a perspective for a thorough-going improvement on what comes out of more-or-less capitalist markets.
Consider the context of Robinson's Ely lecture. Although she had already developed a theory of stagflation, she couldn't have known how poor western economies would perform over the next decades. So at the time of her lecture, the second crisis of economic theory might have been more readily apparent than the first.
It seems to me that both crises are evident today. The world's economic problems are not only how to get people back to work during this worldwide global downturn. We also need to reorient the world's economy to operate with more sustainable and renewable energy resources, encourage the production of more public goods in many economies, decrease the workweek, etc.
- Joan Robinson (1972) "The Second Crisis of Economic Theory", American Economic Review, Papers and Proceedings, V. 62 (May): 1-10