Acquiring a GPS signal

Lately, I've come to realize that certain GPS units (including the Garmin Forerunner 305 and the i-Got-U 120) really only acquire the initial GPS fix when the devices are stationary. This can be a problem if I walk out the door and want to start tracking. Despite giving the units ample time to acquire a signal, they just never get one. Both units, I believe, use the SIRFStar III chipset. Is this issue inherent in this low power chipset or does it happen in all GPS units?

I've seen this behavior in USB GPS sticks as well that I think use the same chipset. Does anyone know if there is a way to make these units acquire the initial signal while moving? Once they get the signal, these units all work fine moving.