It depends on the cover material. Polyester is one of the most popular fabric materials for furniture covers. However, this material is also prone to discoloration. On the other hand, some fabric materials are less prone to discolorations such as polyethylene or non-woven 3-layer fabric.
In other words, the more durable and denser the fabric is, the less likely it will colorfast. However, we should always remember that all types of fabric will eventually fade over time, depending on how you apply proper care for your covers.