If the info at Guitar Wiring is what you've got, the pot and the capacitor are about the only components associated with tone control that might be likely to fail. You can also refer to Wiring Information for Humbucker Pickups which gets you a .pdf that might be easier to save for later.

With some potentiometer constructions, it's possible for the "wiper" to be bent so that it doesn't contact the resistance element it's supposed to wipe against. If this is the problem, you'd probably need to get the pot out of the guitar to do any "fixing" on it, and pots are usually cheap enough that if you've gone to the trouble of getting it out you'd want to replace it rather than messing with trying to make "adjustments."

As Foolestroupe indicated, cleaning the pot "wiper" with an appropriate lubricant or "contact cleaner" solution may work - if the wiper is in place and isn't making good contact, and if the pot is a sufficiently "open" type that you can get the solution into it.

Although it's rare, capacitors can fail. If this is the problem then replacement of the capacitor is the only thing that will help.

A "cold joint" in the wire connections could have lost it's electrical connection, in which case re-soldering may be all that's needed. Sometimes just "wiggling" the wires will show which one isn't carrying the signal, but it's possible to have a fairly sturdy "mechanical joint" without a good electrical one. A volt-ohm meter judiciously used is usually the best tool for sorting out whether this is part of the problem.

As also noted, sometimes a knob loses "traction" on the pot shaft, so that turning the knob doesn't turn the shaft. You can pull the knob off and try turning the shaft directly with your fingers to verify that turning the shaft doesn't change the tone. The knob may have a "set screw" that can be tightened (and/or replaced); but if it's a "friction fit" knob you probably would need to replace it.

Having a crossover switch set wrong might make everything sound a little like it's at max treble(?) even if the tone control is working - on some guitars.

John