The high limit stat which is now an integral part of every rod thermostat is pre-set to operate at 80 -85 deg C it seems you have either a temperamental one which is tripping an lower temperatures or there is something else which is causing the heat to build-up around this area.
I would normally change it as a first action to ensure you haven't just got a rouge one & set the control stat to 60 deg's C (the water stored in the cylinder must be above 55), as these are low cost items. As this has been already been done I would be looking at the wiring connections to ensure they are made correctly any poorly made connections can cause heat to be produced when the immersion is switched on. Make sure there is nothing covering / insulating the immersion cap so any heat build up inside can be lost.
You could try a different make of thermostat so long as they are the same length there are interchangeable, failing that its a new cylinder with them on the side or an anti-stratification pump.