Plant dyed fade over time. The more light they are exposed to the faster the fading goes. What was dyed on a large scale in historical times was wool and silk. Linen is difficult to dye, unless it’s blue.
Sometimes you are lucky and can see the backside of an old textile. The backside have often been protected from light and are therefore of stronger colours then the front side.
Here- a gilded leather embroidery dated to mid 15th century. Skokloster 2, today in the collections of Historiska museet, Stockholm, Sweden. To the right you can see the front, and in the middle the backside. Compare and see for yourself.