Now here's one of the most striking facts about US business cycles. When the unemployment rate does rise by more than 0.6%, it keeps going up and up and up. With the exception of the 1959 steel strike, there are no mini-recessions in the US. The smallest recession occurred in 1980, when the unemployment rate rose 2.2% above the Carter expansion lows. That's a huge gap, almost nothing between 0.6% and 2.2%.
It is possible that the cause of this is the way that recessions are defined. A loose definition is two consecutive quarters of negative GDP growth. (The actual definition is that "The NBER will know it when it sees it," but the loose definition works well enough.)
The point here is that a recession is defined in terms of a shortfall of growth from zero. In an alternate universe, you could define a recession in terms of a shortfall from trend. Last time I looked at this, which was more than two decades ago, in the alternate universe recessions are no longer all short and steep and recoveries are no longer all long and steady. Instead, relative to trend, the behavior of GDP is fairly symmetric. Periods of above-trend growth are about as long as periods of below-trend growth.
In the alternate universe, you would define a recession as two quarters of below-trend growth. Some of these alternate-universe recessions probably would have increases in unemployment of small magnitudes. In some sense, the real-universe definition of a recession tilts the statistical playing field to make it more likely that one will observe only "big" (in terms of unemployment) recessions.
In short, I suspect that the absence of mini-recessions is not informative about our macroeconomic theories. It is informative about the way in which our use of zero rather than trend growth as a baseline affects the statistical properties of recessions.
UPDATE: See Dave Schuler's graph. Looking for years when GDP growth was below the trend line but we were not in an official recession, I see mini-recessions in 1968, 1994, and 1996. If you think we should see more mini-recessions, then remember that these data are smoothed by looking at annual growth rates. Quarterly data might show more mini-recessions, and if you had reliable monthly data they might show even more. I will grant that we don't see the mini-recession phenomenon in either payroll employment or household unemployment rates. To me, that says that employment relationships are sticky--there is a fixed cost to breaking them and a fixed cost to creating them.