This depends on the quality of the rubber mulch. Good quality rubber mulch uses a high quality color coating that is designed to withstand the elements like a good house paint. It is engineered as an outdoor product to withstand both hot and cold weather along with sun exposure.
Many manufacturers will provide a 12 year color guarantee. In most applications the color will last for more than 12 years. The color guarantees typically allow for some level of color reduction prior to 12 yrs as expected. Exposure to harsh chemicals used in landscaping, roof cleaning, and other applications may cause pre-mature discoloration and aren't covered under guarantees.
To help maintain color, a quick raking every few years helps bring fresh rubber mulch to the surface. After a number of years, topping off the rubber mulch with a small amount of new product will instantly refresh your landscaping and further extend its life.
A high quality rubber mulch will outlive most home ownership and its color will last many many years providing an excellent return on investment over wood mulch.