What is causing the stains on my house ?
Iron oxide, also known as rust.
Also known as rust, in different forms.
I have heard from readers that rusty lath is a huge problem in your state, Florida. The downspout here has been clogged up apparently for a long time. Water running out from the joint at the downspout and the elbow has deteriorated the stucco so bad that the lath has rusted through.
We used a sand blasting sand , that is crushed quartz from New Jersey in our finish coat that developed spots in the finish coat within a month, especially where the wall got the most rain. This was obviously from when the sand was crushed or quarried, small particles of steel from the machinery got mixed in the sand, and later became rust stains. The stains didn't look bad on an orange stucco house we did, but looked terrible on the green wall we did. We ended up re-coating the green wall for free. Iron oxide was also a problem for Finestone and aggregated finishes years ago.
There used to be a chemical, oxygenated bleach, that took off rust stains like magic. Now oxygenated bleach is made from grapefruit and isn't nearly effective as the old oxygenated bleach, which is considered a hazardous chemical and isn't made anymore.
I hate to say it, but your only solution here is probably painting.