Firstly im not qualified to give electrical advice, and googleing anything i suggest is worthwhile before committing, that said
...
if the element is switching on/off then its highly likely that its got some over boil or boil dry protection
the first thing to check is if the element has any burnt on crud as this will help it overheat, so scrub back to shiny metal, vinigar, lemon juice, citric acid, or even kitchen kettle descaler will do it..
then if still cutting out look for the thermal fuse and or thermal switches. open the base with the power off and unplugged. one or both will probably be attached to the element base
thermal switches generally look similar to:
its probably the thermal switch thats at the root of the problem as it can switch back on once cooled sufficiently, thermal fuses on the other hand tend to blow and no longer work at all.
you can either unbolt it from the base plate or bypass it and connect its two connecting wires however your advised to use a High temperature connector, the usual leggo brick style connector could easily heat up and melt its plastic coat.
post pics if in doubt, and always unplug anything before you open it...
edit you can also buy a suitably rated replacement thermal switch for a quid or 2 go for something that is Normally Closed NC, rated for at least the same as your element i would go higher .. and select a temperature that it will switch off at like 140C or more..
http://www.ebay.co.uk/itm/Thermal-Thermostat-Temperature-Switch-NC-or-NO-Range-from-50-C-to-150-C-/151084725893?_trksid=p2141725.m3641.l6368