Stain is just a surface and a very temporary fix. Stains do not usually contain synthetic iron oxides, which are very permanent and very ultra violet resistant. Iron oxides come in yellows, reds, browns and black. They do not come in greens or blues. Blues and greens are either shortlived stains (cheap) or very expensive metallics (chrome, etc.).
It is very rare for the pigment in a concrete block to fade and the fading usually appears because the concrete itself gets lighter as it cures. Some colore are pron to fading because of the raw material - cheap carbon black is substituted for black iron oxide and dyes are used instead of oxides. Common dyes will fade and be suject to ultraviolet rays. Carbon black will just wear off, so you don't see it any more. Very often dark mortar will use carbon black, so it can fade.
Burgundy could be a color that can be difficult without the right aggregate. Because of this, and the fact you do not know what pigments (may contain blues or cheap blacks) were used and why it is fading, I would clean the wall well to see what you have as far are as clear color and unuformity. Soap may be better than acid unless the acid is very diluted.
Daryl's suggestion is the best. You don't want to throw on just anything without really looking at it.