Which fuse are you referring to, what number and which fuse box? Since you don't answer, there is a problem with the lighting control module if your battery is running down and the lights are the problem. The lighting control module will shut the lighting circuits off after a short period of time.
That's the one that goes straight to the lighting control module, it feeds the on demand lighting. Includes glove box, trunk, vanity lights. The control module is supposed to disconnect the power to all lights in a short period of time, around 5 minutes. If the battery is going dead it has a problem between the fuse and the light control module. The Lighting control module should not be discounted, because they do go bad as well, but usually has different symptoms.