Can a slow small plane, flying at a few meters above the ground, drop to the ground if the headwind abruptly stops? Why do I ask this question? Because Wilbur Wright sent a letter to Georges Spratt (an aviation enthusiast he personally knew) saying that his plane, Flyer II, once in flight, accelerated easily to 45 mph, by itself, after reaching 30 mph. (The plane had no throttle.)
I know that once in flight, the airspeed of a plane is independent of the headwind, so it simply does not matter how fast the wind blows from in front of the apparatus. Those lulls in the wind Wilbur feared about would not have had an impact on the course of the aeroplane unless the wind suddenly dropped in intensity (this is more a theoretical case). Only then for a short time the airspeed of the plane decreases to its former airspeed minus the drop in the headwind speed, but the plane regains quickly its former airspeed.
The question is, can a low flying plane really touch the ground just because the intensity of the headwind diminishes?

We have made forty five starts with our 1904 Flyer. Unless the relative speed at starting is 27 miles in a calm and two or three miles more than that in a wind, the machine will gradually slow down till unable to fly. After the relative speed passes thirty miles the velocity accelerates till a relative speed of 45 to fifty miles is reached. We found it difficult in practice to get a speed down the track greater than 20 miles an hour, so that unless we had a wind of about 10 miles we were not sure of being able to fly for a lull in the wind would let us drop below the real flying limit. … We have now finished a starting apparatus which gives a speed at start of 27 miles an hour in a dead calm, and expect shortly to begin circling. (Wilbur Wright, “Letter to G. A. Spratt”, Dayton, Sep. 10, 1904)


Source Small plane flying at low altitude.
Update:
The topic Does a sudden drop of the velocity of the headwind affect the airspeed by lowering it? and its explanations do not answer my question. I was already aware that a sudden drop of the headwind intensity reduces for a short time the airspeed of a plane and I have already written this thing to make it clear I knew about this phenomenon.
The plane of Wilbur flew a few meters off the ground.
So, assuming Flyer II traveled at an airspeed of 30 mph against a headwind of 10 mph and suddenly the machine entered a region of perfect calm, its airspeed would have reduced to 20 mph instantly, but did the plane need to drop more than a few meters to regain its former airspeed of 30 mph?
Yes.  The theoretical concept of &quot;moving with the airmass&quot; essentially says that for any given constant wind or no wind, airspeed is dependent on thrust and drag and reaches a steady state.
However, in nature, especially close to the ground, obstacles such as buildings, trees and hills can make airflow anything but constant.
This is why the modern aviator adds a little airspeed when landing on windy days.  A gust or a lull can momentarily change your airspeed faster than the plane can restore its thrust/drag balance.
Wind shears are an extreme example of this.  Were it not for the wind, flying that Cessna would not be more difficult than driving a car.