Pickup fading in and out

Probably - but if it's an active guitar, then it could also be a power supply fault, and the capacitor on the DC is fine, but when the DC vanishes due to a dodgy connector, this discharges the capacitor slowly and it fades out. A fault with a few causes.
 
How long does it take to fade out? If you unplug it, then plug it right back in, what happens?

Is it an active guitar? My first thought would be the battery.

Not active? Then, probably a cap.
 
When you say fade, is it gradual or does it cut in and out? I've had selector switches go bad where it just cuts out. I had a volume pot go bad and it just cut the level drastically unless you hit the right spot. Changed the pot and all was fine.

I don't think I've ever had a tone cap go bad. Those things are rate for anywhere from 50v to 400v, and we're sending mV levels through. Besides, a tone cap only bleeds off high frequencies for the signal. Turning the tone control all the way up essentially takes the cap mostly out of the circuit, since you're putting 250 to 500kOhms in the R/C circuit.
 
It's possible that there is a soldering problem.

Here's a good read how as to how someone else experiencing the same problem of fade in/out eventually discovered what caused the problem and what he did to fix it.

 
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