It's most likely that it's the contacts on the magnetic switch (the thing that the capacitor is soldered to). It's basically a long tube that runs down the centre of the element with a sliding magnet inside and a rod and spring to actuate the contacts. The magnet is attracted by the slug on the back of the tip, closing the contacts. When the slug reaches its curie point it stops attracting the magnet and the spring opens the contacts.
It's an accurate and reliable system, but the switch contacts themselves can get dirty, or the magnet-switch assembly can go faulty (magnet sticking or whatever) or just 'tired'. Once you've checked all the other things, cable connections, plug, heater continuity etc then you can try opening the top of the switch and try cleaning the contacts.
Sometimes it's as simple as the handle not being assembled correctly, the whole switch assembly is sprung loaded so that it can slide to touch the rear of the tip. If the assembly sticks too far back in the barrel then the magnet will be too far away to be attracted by the slug. As you insert the tip into the end of the element you should clearly hear the click of the switch closing, if that doesn't happen then there's a switch problem.