All that's been established so far is that the problem is nothing to do with the battery.
Have a close look at the front of the controller, just outside the dial, just below half way down on the right hand side. The microswitch that switches the power for the timer is just behind here, and if it overheats and fails will cause some distortion and discolouring of the plastic front.
Could be as simple as each immersion heater has a local isolator switch, and the one for the timed immersion is switched off.
Unless the immersions are really old, they will have some kind of overheat protection built into them, in case the thermostat fails in the 'on' position. These occasionally trip for no apparent reason, so it could be just this needs resetting.
The types vary, but the cover over the immersion head will need to be removed to check. MAKE SURE THE POWER IS OFF. If the single nut holding the cover is loose or even missing, it's a good indication that this safety cut out regularly trips and it, or the main 'stat, is probably faulty.