The middle pickup on my Epiphone S600 does not come on when the 5 position selector is in the middle position. I cannot tell if it ever comes on. Also, the volume control closest to the tone control does nothing. How do I figure out what is causing the problems.
It's most likely a loose connection in the guitar's wiring, or a wire that has become lose and fallen out completely. Believe it or not, some of the soldering jobs for electric guitars do not meet IPC standards! The horror. In other cases, wear and tear can take its toll but if the job is done well it shouldn't need revisiting more than once a decade.
If you're feeling bold, and if RadioShack still exists (does it? last I heard it was holding on by the thread of a fingernail) you can (carefully) open the casing with a small screw driver and try to solder it up again. Obviously, only do this if you feel you know what you're doing and are willing to take the risk. And safety precautions apply as they would for doing any soldering work with a hot iron. And other electric safety precautions are advised. For instance, the guitar should not be plugged in when you operate, etc.
It's probably a better idea to take it to a guitar repair shop. Be warned though, a shop that does more business in amps and electric guitars is likely to be a better choice than a luthier focusing on acoustic instruments. In at least one major city, I've been to almost every available guitar repair shop and almost none of them could solder properly.