Some hair especially body hair regrows after trimming but stops growing after a while. What is the mechanism behind control of hair growth and how is the length limit determined?
Hair grows from the follicle; there is no way for the follicle to determine if the hair tip is trimmed or not. This is unlike plant shoot/root growth that happens at the tip. Also there is no signaling from tip to follicle.
Hair growth has four stages: Anagen (Initiation), Catagen, Telogen (resting) and Exogen (falling off). Initially the primary follicle is formed during development of the skin, after that the hair growth continues in a cycle. In other words the old hair shaft is replaced by a new one. The period of the cycle (or how fast it happens determines the final hair length); the faster is the cycle the shorter will be the hair (you may note that certain people have a very short head hair even when they do not trim). This is because the old shaft doesn't get time to grow before it is shed and replaced by the new one.
From: Stenn & Paus (2001)
From the same source
Because there is a limit to the time a follicle stays in anagen, there is also a limit to the length of its product, the hair shaft. The anagen phase has been divided into six subphases (64, 359). Except for the last subphase, anagen VI (the duration of which dictates the shaft length), the length of the anagen subphases I–V does not differ substantially between follicles from different regions (490, 565).
Because the actual length of a hair follicle does not appear to dictate the length of its shaft (rather the duration of anagen determines hair shaft length), it is tempting to speculate that the subcutis offers optimal growth conditions…
Although influenced by environment (light, temperature, and nutrition) and systemic (endocrinological factors) parameters, it is generally believed that there is considerable innate local control of hair shedding; each fiber grows to a specific length, for a specific period of time, before being shed
Think about it statistically. If you cut your hair short and it grows out, it's because the length you cut it to was shorter than the average length that any strand of hair is likely to grow to before it falls out. As your hair grows out, it approaches that length.
(This is a simplification but is illustrative of the process.)
I still take in consideration the odd that the hair growth regulation might be length based and not only time based. The hair total life cycle is certainly time based in that it will fall off and shed regardless of how much you cut it and its current length. That's why you see them especially hair, shedding of any length. They are, as stated here, at different stages of their life cyclr, different ages, otherwise they'd fall all at once. Possibly not so for its growth phase, which might be influenced by their length. I know it's argued that hair just sheds at a given time after a dormant phase regardless of its length, which is true, but also that it doesn't grow back to its full length but to its remaining length/time before reaching its resting phase and that if the hair collectively grows back to that point, it's because younger hair surrounding it which were shorter before the longer ones got cut, made it to that point. Yet hair like eyebrows and eyelashes seem to have most of it in dormant stage, sharing a similar length, before shedding. It would take much longer for them to grow back if all this dormant hair had to shed before growing again. We should consider that cat whiskers are just evolved and very sensitive hair shaft. The shaft is still dead but it's the follicle nerve which definitely uses their lenght to obtain all kind of info about the surrounding environment, especially spatial clearance. So it doesn sound so impossible for a follicle nerve to detect cuts and a change of length of its psysical support.
Another thing is that trimming your hair reduces splitends that may cause hair to continuously break at the tips and thus not allow the hair to grow to its optimal length. By trimming the tips you are reducing breakage.
@WYSIWIG's answer seems to imply that hair has a natural length, but there is more to it than that.
My arm hair is normally about 20 mm long. However, when I had a full arm cast on one arm for four weeks, it radically affected hair growth of that arm where covered by the cast. After the cast was removed, most of the hairs were 45–50 mm long and considerably thicker. The covered portion looked closer to money arm than human.
Well, maybe not that extreme. It took about twice as long to return to normal than it took to "monkeyify".