It is not a rule that the personal saving rate rises during a recession, just in this one. Take a look at the cumulative trajectory of the personal saving rate for this Great Recession compared to its predecessors, as represented by the "average recession" since 1960.
The chart illustrates the cumulative growth of the saving rate throughout the recession period and during the twenty-four months (of recovery) following the recession for the current cycle and the average over the latest 7 cycles. Note: convenience only, I call the end of the current cycle at point 0 or June 2009. I do not believe that the recession is actually over in June.
Recently, the average saving rate, which is estimated monthly by the Bureau of Economic Analysis, surged since the onset of the longest recession in the post-War era. Consequently, the sharp ascent of the marginal saving rate is wreaking havoc on personal consumption spending, and thus, GDP.
Interestingly, current saving trends mark opposing behavior relative to the "average" recession occurrence, which is the indexed trajectory of the average saving rate spanning the 7 recessions since 1959. The saving rate drops during the average recession, and stabilizes thereafter. So far, the saving rate has a -50% correlation with the saving trend during "average recession", and is moving against the broader historic trend. If saving continues its ascent, one can discount quite significantly the possibility of an "average recovery" to a recession this deep (i.e., V).