Simon,
Yours is not such a big problem and I believe you need to spray some contact cleaner at the right spot which can resolve your problem. In most cases variable resistor has a life span and pending how often you use it. I am not sure how many deckers is your variable resistor, I think you can get one or equivalent off the shelf. I have repaired quite a few of our church amplifiers and only one (10k double decker) was not "repairable". I got an equivalent one and replaced it. If yours is coupled with remote motor driven, then it may be a bit difficult to install an equivalent. Best is to forego the motor driven type and go fully manual.