Usually that kind of a “stain” is due to a slight difference in stucco mixture/texture in that location.
At the time of construction, someone came in and either purposefully (plumber) or accidentally (roofer) damaged the stucco there and the stucco guys were able to “repair” it quite quickly (all things considered) so that there is little if any visual or noticeable difference between the repaired area and the area that was not repaired.
However, the repaired area was from a different batch of stucco mix, and since no two batches of stucco are exactly the same–ever–the batch used for the repair has slightly different wetting/drying characteristics.
This is why we endeavor to make enough stucco to completely stucco the home at one time. If we fail in our measurements there, then we at least use the different batch on a different wall. Never put two separate batches on the same wall because they will cure at different rates, possibly creating a crack in brand new stucco between the two batches, and will contract/expand at diffferent rates, also creating a crack between the two batches. It took me forever to explain the concept to the SOTB laborers until I demonstrated it on a 9-square-foot section using four different stucco batches. However, sometimes a picture truly is worth a thousand words, especially when one doesn’t understand those words because they are in a foreign language.
Ultimately, if the two batches of stucco mixture are too different, resulting in their wetting/drying/expanding/contracting characteristics being vastly different (all things considered), then the batch/area that stays wettest the longest will blister and slough first. This is why you occasionally see a blister fifteen feet from the ground, waaaaaay too far up to have been caused by absorbing ground moisture. I’ve usually found that the “stain” in your photo occurs near second-floor plumbing, especially if there was a spa tub installed in that location, and near second-floor windows. That’s because the plumber had to do some repair work, or install special plumbing for the spa tub, or a window was damaged by the roofers and had to be replaced, all resulting in damage to the stucco and repair with a different batch a few days or weeks later.
KB Homes here now understands proper stucco installation, courtesy of yours truly about four years ago, which could be the reason that KB Homes here regularly ranks at or near the top in homeowner satisfaction. And the #1 complaint? Stucco cracks. Indeed, they are ugly, but they also are not necessary if one understands stucco. Kind of like pool cracks, except not quite as serious as pool cracks.
With regular homeowner monitoring and maintenance (which should be done with stucco anyway), it should not prove to be a problem. But, again, regular homeowner monitoring and maintenance is key. Advise your client that stucco will crack and that he should walk around the home (or have a stucco professional walk around) at least once a year, note all the cracks, and patch/repair or otherwise seal and weatherproof them.
Just like inside, those exterior cracks usually will occurr diagonally at door and window corners (KB Homes here has learned how to prevent those common cracks, as well) and in large expanses of wall space, like on a two story building. Even if those cracks become long and wide, like from a first-floor window to a second-floor window, it typically will not be a cause for structural concern. It’s just a massive expanse of stucco that cured at different rates, just like a large expanse of concrete (KB Homes has learned how to prevent common concrete curing cracks, as well–Hmmm. I hope they paid me well. Hey, they did. Yahoo!!!). But as I educate my Clients in my reports, a common concrete/stucco crack can become a major concrete/stucco crack if it is ignored. In the case of stucco, ignoring those cracks can allow moisture to penetrate into the wall framing, and we all know what could happen once moisture gets into the walls. Uh-oh.
And why did I take such an interest in KB Homes, while ignoring all the rest? Because I had a KB Home.