When I was doing new construction down there I would regularly demand a two week "water cure" before I would touch a house. Someone needed to hose down the entire structure twice a day, every day, for two weeks. The water draws out the lime that stucco guys over-use to speed their jobs. After that two weeks the stucco is pretty much as hard as steel.
Once in a while, when repairing severe efflourescence (to the point where the brown coat was sloughing off the finish coat, not unlike Vin's 1st pic), I would scrape the released coat of stucco and after the acid-cleaning would do a water curing of the affected areas. Time consuming, but those areas were never a problem again.
Retaining walls are the worst for efflourescence, especially when stucco'd over...
pH testing with phenolphaline (sp?) is a must, water cured or not...If the test shows positive, reFUSE to paint...