How can I determine what is wrong with my lighting circuit?
Sounds like you have a break in a wire or a corroded terminal somewhere. Usually, breaks and corrosion happen where the wire connects to things, and not in the walls.

So first thing to do is to take each device off (switch, outlet, light) and inspect the wire that you can see for break. Inspect the device, too, especially outlets with back-stab connections. While you have the outlets out, switch from back-stab to screw terminals.

If you can't find the problem there, it's time to call a professional. Intermittent connections like this can be dangerous because broken wires and the like can cause arcing, heating, and fires.