It really does depend on the thickness of the photo emulsion and the print ink. I've done silk screen prints where 20 prints were managed with little detail loss. The thing with the silk screens is that as a woven cloth, it's prone to slightly stretching with each pass of the ink, so the emulsion gets thin in spots rather quickly.

I would imagine that on the big industrial printers that are using a metal mesh screen and thicker emulsion, it's maybe closer to 50? Usually in a print shop doing a big run, there'll be four or five screens made for each print layer so when one gets worn, it's replaced in the printing rack. It really is an artform.