the dimming is controlled by the electronics inside rear view mirror which will send signals to the side mirrors for dimming.
to test, turn on your car's engine and shine a torch at the small "hole" on the rear view mirror and cover the sensor at the rear of rear view mirror. if it does not dim, it might be the electronics inside the rear view mirror which has failed.
you can either
1. live with it
2. spend a few hundred $$ to buy new one from stockist
3. spend up to $100 to buy used from eBay
you may want to have a workshop check it out by swopping a working part to test and make sure that it's the mirror that failed and not some other car module