Maya blue is an organo-clay artificial pigment composed of indigo and palygorskite. It was invented and frequently used in Mesoamerica in ancient times (eighth to 16th centuries). We analyse in this paper one of the characteristics of Maya blue that has attracted the attention of scientists since its rediscovery in 1931: its high stability against chemical aggression (acids, alkalis, solvents, etc.) and biodegradation, which has permitted the survival of many works of art for centuries in hostile environments, such as the tropical forest. We have reproduced the different methods proposed to produce a synthetic pigment with the characteristics of the ancient Maya blue. The stability of the pigments produced using either palygorskite or sepiolite has been analysed by performing acid attacks of different intensities. The results are analysed in terms of pigment decolouration and destruction of the clay lattice, revealed by X-ray diffraction. Palygorskite pigments are much more resistant than sepiolite pigments. It is shown that indigo does not protect the clay lattice against acid aggression. We show that Maya blue is an extremely resistant pigment, but it can be destroyed using very intense acid treatment under reflux.