I would agree David, the 12v power to light the LED and control the temperature is supplied by it's own onboard 12v transformer, this then would quite possibly lead to the LED dimming very slightly.
The common problem though is failure of one or more of the three relays that switch the various power outputs, most commonly the 2kw relay fails first. Not total failure so you will hear them 'click' but burnt contacts preventing current flowing once the relay switches on.
Truma in the last couple of years have 'uprated' the relays from 10A to 16A in the hope of curing the problem but it would seem this is not the solution.
The real problem is to protect the 12v circuit a diode is used on each relay, this does the job it's there for but has the side effect of slowing the time it takes for the relay to make/break, this in turn causes 'arcing' and subsequently burnt out contacts. This apparently is then further aggravated by legislation banning Silver/Cadmium in favour of Silver/Tin for contact material, Cadmium being more durable than Tin in this application.
One other more simple possibility is the presence of two thermostats, one of which has the habit of self destructing! and would explain no heat output on any setting.
These can be seen behind the gas fires exhaust flue pipe albeit the fire probably needs to come out for access, you may then want to leave all this to a competent service engineer