The human respiratory rate varies by person (and is dependent on age, health and level of exercise). According to Wikipedia, the resting range for a healthly adult would be between 12 to 18 breaths per minute (i.e. a 50% difference from low to high). For the elderly, the upper range is 10 to 30 breaths per minute (i.e. a 200% difference).
In addition, in order to measure any significant time period, you would need to stay in a resting state for the entire time while counting your breaths. It would be nearly impossible to use to measure the time taken to perform any strenuous activity because a) you breathing rate would vary and b) it would be difficult to keep a reliable track of the breaths taken. There's also the possibility that monitoring your own breathing rate would affect the rate (i.e. your attempts to keep your breathing steady might actually change the rate).
So, ultimately, it would be difficult to form a reliable universal time measurement based on something that would vary so much. It might be useful for personal use to compare a couple of events of short duration but it wouldn't be much use to pass measurements from person to person.