Bad ignition switch? Maybe your ignition switch is loosing contact in the "RUN" position. Essentially when you turn the key first you go to the "ACC" in which the accesories in your car get current, next step is "RUN" which adds the engine control circuits & ignition to the current. Last step is "Start" where the the accessories circuit is cut off and the starter solinoid is activated.
If this is the case your indicator lights (check engine, brake, ABS, etc..) probably won't come on until you turn the key to "START". Whereas if it is working properly they will come on when you get to the "RUN" position.
If it's not your ignition switch, it might also be a relay related to the ignition circuit.