In our experience, render doesn’t generally tarnish, however with age and prolonged use, the surface can pick up small marks from debris or wear and tear as any surface would do.
It is worth noting that if you find that the render has got particularly grubby, a decent quality, silicate-based masonry paint is the easiest way to get it looking good again. Some marks can also be removed by gently wiping the area with a damp cloth.