How long do the pulses last?
I'm thinking maybe if the pulses last, for example, 100ms then you can have the board sleep for 95ms, wake, check then go back to sleep without missing a pulse. Further to that, if you know there will never be, for example, more than 1 pulse every 15 seconds then after you detect a pulse you can sleep for 14 seconds knowing that there won't be a pulse in that time.