Yes, it should break eventually. Not sure about cycles though... I think humans have a tendency to see/hallucinate cycles from random variation.
This one might be done, however. I suspect that February 2010 storm may have been our last best chance of breaking this one; however, despite over 20" of snow, it was split fairly evenly over two days, keeping the calendar day total under one foot. Definitely can see each period getting longer... records began in 1880, first streak ends in 1884, then 1890, then 1901, then 1902, then 1913, then a long break ending in 1942, then 1950, then 1960, then 1966, another long break ending in 1993 (Storm of the Century) and none thereafter. If it is the last calendar day with one foot of snow in Pittsburgh history, fitting for it to be the March 1993 Superstorm.