Why is it said that it takes more energy to let a house cool down and heat up again, compared to keeping the temperature constant? In nearly every webpage that I read on the topic, it is recommended to not let a house cool down over the day (even if nobody is there), but to instead keep a constant temperature.
This is reasoned by the sentence "It takes more energy to heat up the house again, than you would save by not heating it for a certain amount of time".
To me, this is unintuitive behaviour, to say the least. The house (or the flat) loses energy to the surrounding buildings / air / ground by conduction, by air movement, and by radiation. In any of those heat-transfer-mechanisms, the energy loss will increase with increasing temperature of the house.
So my question is: What am I missing? It can't be that I'm right and any plumber / heating technician is wrong.
Could the problem of overshooting temperature during the heating explain this? If so - why? The energy that is too mutch stays in the house.
To keep the house at a constant temperature, I have to balance out the energy loss.
To reheat the house, I have to deposit the energy in the house that was lost during the cooling.
Because of the mentioned temperature dependence of the energy loss, reheating to temperature $T$ should take less energy than keeping the temperature, because less energy was lost.
I'm well aware that houses shouldn't not cool down too much (because of freezing pipes, moisture in the walls, mold, etc ...). This should not be the topic of the question. In case it should matter, I live in germany.
 A: It is incorrect indeed. The house is losing heat at a rate $\dot q = k(T_i-T_o)$, in a simplified point of view, so the higher the difference between inner and outer temperature the higher the heating cost. From this point of view it is better to keep it at a lower temperature. As long as you make sure it is heated up in time for when you use it that should be fine. Note that your experience of comfort depends on air temperature and on wall temperature. If the walls are cold you will experience cold even if the air is warm. It will take some time for the walls to warm up and the house to be comfortable, and more so if you kept it at a low temperature. Switch to low temperature when you leave and switch back to room temperature one hour before arriving seems a good approach. Watch out for freezing of pipes, though.
A: Spherical horse in vacuum
The obvious answer that constant heat losses exceed the energy expenditure for warming up the house from a lower temperature is based on many simplifying assumptions that may or may not hold in real life - depending on the climate (typical temperatures, huminity), house construction, and the type of heating used.
Factors to consider
Without taking sides with pro- or anti-constant-heating crowd, let me point out a few possible complications:

*

*Non-linear heat losses, e.g., due to convection or radiative losses, may change the situation quite drastically, although one may expect them to be higher at higher temperatures.

*Phase transitions - as I already remarked in the comments, usual suggestion is to keep the temperature at least above the freezing level, since melting iced tubes could be both energy-consuming, and cause potential physical damage.

*heater inertia and non-linearity - a realistic heater effects. Here much depends on details and quality of the heater. Probably not relevant when using modern equipment.

*non-uniform heating - much depends on how fast the heat diffuses over the house - the heater might have go in overdrive before all the corners are equally warmed, hence excess losses.

*speed of heating - if it takes a few hours to warm up the house (e.g., when using a fireplace)

*temperature control - another fact relevant to a fireplace - you may not be able to control the temperature, leading to overheating and losses.

The reality
Overall, with modern equipment, isolation, etc., it is better to lower heat, while not allowing the temperature to fall below the freezing point.
A: 
It can't be that I'm right and any plumber / heating technician is wrong

It sure can.
The first order physics are really quite simple: the energy that is lost is the temperature difference between the inside and the outside divided by the   thermal resistance of the house. You can save energy only two ways: increasing the thermal resistance (better insulation, closing & sealing doors and windows, etc.) and by lowering the inside temperature. That's all there is to it.
There are some second order effects/considerations: you certainly don't want so far that pipes start freezing and/or damage occurs. A heating cycle can potentially overshoot a bit and there is the discomfort of coming home to a cold house.
I'm guessing that the rumor is mostly fueled by "that's what people want to hear": they like the idea of a warm and comfy house and don't want to wait for it to warm up.  However, these days all of this can be easily mitigated with a smart thermostat.
