You can sometimes recover a poorly operating potentiometer (variable resistor on the other end of the volume knob) with a specialist cleaning spray. Maplins will sell this and possibly even a replacement pot.
Otherwise you will need to unsolder the broken one and fit a new one.
It may not be the pot causing this problem but as it's a moving part it's odds-on that it is the cause.
To make the repair yourself you will need to be handy with a soldering iron and have the ability to source the right potentiometer both electrically (relatively easy) and physically (could be more difficult to get one that fits).
I bought a cheap Pure DAB form Tesco last year for under £50 - white plastic - in the bathroom - perfectly adequate.
Good luck...
Peccavi
February 2009