Automatic Stability Control and brake warning lamps are both lit

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Car will shudder, feel like something is grinding and then both the Automatic Stability Control light and brake warning light will remain lit. Once car is shut off and sits for a while and then is re-started, the warning lights are no longer lit. After driving for about 20-25 minutes, the car will shudder, grinding feeling returns and above lights will light. Speed sensors on all four wheels have been replaced. What's wrong?