Gas fridge won't light

We have an Autosleepers Ravenna. I think the fridge is a Dometic. The problem is that on the gas setting, when we depress the button, it clicks away for a while then lights, but as soon as we take our finger off the button the gas goes out and it starts clicking again. I'm guessing that there is a problem with the thermocouple. The people we bought the motorhome from had clearly had problems with this, as their advice was "keep trying - it could take up to two minutes, but it will work eventually". But now we can't get it to stay lit however long we try.

Has anybody else had this type of problem with a fridge, and if so, what was the solution, and how much can we expect to pay to get it fixed?

Many thanks in advance.