You might want to start by looking for a loose connection. What are the chances of both parts of the ballast burning out at the same time? I have found my fixtures made by some manufacturers are not well built although the component parts seem to be fairly good quality. When that happens, simply making good connections instead of the ones they made for you, is often enough to get a nice reliable fixture. If simple troubleshooting of the wiring does not work, try an on line search for fluorescent ballasts and there are tons of vendors who can supply them. I have purchased good ballasts on line to fix fixtures that were actually no good. You will need to access your existing ballast to read the specs on it, so that you can order a compatible replacement. The wattage ratings and type are both needed bits of information. You will also want to leave the fixture laid open and compare the dimensions of available ballasts with the space inside the light fixture. There can be several different sizes in equal rated ballasts. I favor the electronic ballasts when replacing one because they are more energy efficient than a conventional one.
