As other have indicated it could be just a loose wire in your install, if your using a wire harness for those check that your relay is engaging, it as Arth indicated could be a ground, it could be a positive off the battery, it could be your trigger from the bulb connector that is not connected, it could be your relay in its socket is loose. You will need to trace the system to see where you issue is coming from. If your not comfortable tracing and testing your connections have someone who can use a tracer light or a volt meter or just a wire to manually trigger to see where your problem is coming from.
May have a loose wire, bad grounding or a locked up ballast that got corroded.
Same thing happened to me last fall and it was the drivers side ballast. Corroded like heck and it locked up (dead) and due to being relayed it caused the other to shut off.
There are many factors here.
Check the relay, check the connections in the ballast by removing the connections and check the ground.
Almost positive its the ballast or relay