We present a model for the growth kinetics of III-V nanowires which describes the time evolution of the monolayer coverage and group V concentration in the droplet. Special emphasis is put on the stopping effect at very low group V contents, where 2D island rapidly fills a fraction of monolayer and then grows much slower at the rate of the droplet refill from vapor. Such a regime has far-reaching implications in the periodically changing morphology of the growth interface, nucleation statistics, and size distributions within the ensembles of III-V nanowires.