I think the other shields stay up. Only the damaged shield should collapse. I mean each shield is powered by its own circuits so once the shield is overloaded it the circuit breakers would cut in and not dump the overload onto the other shield circuits. It only makes sense. Of course in a dramatic moment the circuit breakers can fail and the entire shield system blows and they all collapse.
Arise, arise, Riders of Theoden!
Fell deed awake: fire and slaughter!
Spear shall be shaken, shields be splintered,
a sword-day, a red-day, ere the sun rises!
Ride now, ride now! Ride to Gondor!
Theoden King: The Return of the King