Why would this microphone only work while touching the volume control?
If it is a grounding issue, touching it could change the amount of hum, buzz or interference.

However you say "It only works if you keep your hand on the volume knob" which I interpret as "there is sound only when the hand is on the volume knob, otherwise there is no sound."

If this is the case, then I'd suspect a bad contact perhaps at the pot wiper, or a cold/broken solder joint that makes contact only when the volume pot is messed with.

You can check this by touching the volume pot with a non-conductive object like a plastic rod. You can use the shell of a ball point pen, or a toothpick for example. If wiggling the knob around with a non-conductive object results in the sound turning abruptly on or off, then you can rule out any influence from your conductive finger, it'll probably be a bad contact.

If the failing contact is at the pot wiper, it will depend on the pot's position. So if the problem does not depend on the pot's setting, it is more likely this is a bad solder joint on the board.