The original symbol representing Second Wind Running Club was a Chinese character, 屁, pronounced "pee", meaning "wind (from bowels)" or, colloquially, "buttocks." The character is apt on a number of levels.
1. Of the "winds" produced by the human body, those emanating from the buttocks are certainly the second (after those from the lungs), and thus the character symbolizes a "second" wind.
2. The character itself has an interesting etymology: