Paper Barriers: When paper is used as the water resistive barrier, it must be overlapped in a shingle fashion (horizontally) and when you have a vertical seam, there must also be overlap. It is also good to have two layers of grade D paper (10 min. or 60 min.)
When there is no overlap, or very little overlap then water can make it's way behind the paper and into the sheathing, wall or inside the building. Single ply paper does not do well either and two plys are recommended, even if you are using a 60 min. paper, for maximum water protection.
Paper for stucco is very cheap and not having adequate overlapping can lead to so many expensive problems later on down the road, it is not worth cutting corners on the main waterproofing element of most stucco systems.
Liquid Applied Barriers: WRB's that are a liquid applied product must be applied in a way that adheres to all of the manufacturer's specs. This includes things like applying the product within the ambient temperature recommended, over an approved substrate, obtaining the required mil thickness (multiple coats) and other elements in order to properly seal the substrate.
A lot of liquid applied water barriers fail for a number of reasons but from my experience it is usually due to improper installation. The two main failures are that the product is not applied thick enough which could result in small pinholes that allow water to get in or applying the material when the substrate is not clean.