"They do not stop drinking."
Translation:Ellos no dejan de beber.
Detener would not be used in such a situation. It is more along the lines of stopping something or someone else. So for example: La policia detiene el ladrón. = The police arrests the burglar. Yo detengo la maquina. = I stop the machine. Dejar is used to indicate someone stopping doing something (an action) himself. Yo dejo de beber. = I stop drinking.
It's one of the "perifrasis verbales". It's just a construction, where the meaning of the main verb in a construction like that gets altered. Dejar de (Inf) = acabar de (inf) = to finish doing something. http://www.materialesdelengua.org/LENGUA/morfologia/perifrasis/perifrasisverbales.htm