The way my car's light-bulb warning light works is that, once triggered, it will stay on until the ignition is cycled through off. I had a bad brake light bulb, and the warning light would come on when I touched the brakes for the first time in the morning, and then stay on.
So, I recommend you check on two things:
1) Make sure the light-bulb warning indicator in the dash still comes on when the ignition key is turned to ON, but before starting the car.
2) Check all three of your brake lights.
One scenario I'm thinking of is that your light-bulb warning indicator bulb has shot.