DA40 Flight Instructor reported the student performing a power off approach touched down 3 feet before the runway.

Narrative

During the last landing back into ZZZ Flight Instructor (IP) instructed the student to perform a power off 180 to the numbers in preparation for a DPE who requires their applicants to do so. IP had mentioned during prior power off 180s; to the numbers; that ground effect is different over grass than pavement. After cutting power and pitching for 88 the student put in flaps early believing we were too high. On final the student mentioned we were coming in shorter than expected. (We had a headwind and increased drag). The student pitched down to gain airspeed into ground effect. Short final IP told SP to add power 3 times but by the time power was added the aircraft sank and touched down approximately 3 feet before the runway. There were no approach lights for the runway. An immediate go-around was initiated and IP took controls to fly back around and land. Maintenance was notified the moment we got back and they inspected the gear. Maintenance said there was no damage or any reason for further inspection. I should have taken controls or verbally commanded 'go-around' when I realized we were going to be a few feet short.