I have to say that what callen says makes sense.
Let's say that we create a spell version of Ward Against Heat and Flames that has a Moon duration. That spell should have it's effect until the moon rises and sets, per the description of Moon duration. There's no implication anywhere that I can see that says that your protection from flames will flicker at sunrise and sunset during the course of your Moon duration.
Or let's take a different example where the flicker might matter more. Say I develop a disguise spell that will make me look and sound like someone else for Moon duration. I develop this spell so that I won't be in trouble if I'm engaging in the impersonation at exactly sunrise or sunset. Again, there's no hint anywhere in the rules that this illusion should flicker at sunrise or sunset. In fact, I designed the spell to have Moon duration just to avoid problems at sunrise and sunset.
So, what if I design a version of Maintaining the Demanding Spell at Moon duration? The effect of that spell is to maintain the concentration of another spell for its duration (Moon, in this example). Just like the two above spells should not flicker at sunrise and sunset, so to should this one not flicker either. I'm not sure why this spell effect should be treated differently than any other spell effect just because it involves concentration.
The fact that there is a mechanism for devices maintaining concentration should not alter the working of a mechanism for a spell effect maintaining concentration. Yes, the rules say that when a device maintains concentration, there is a need to "renew" the concentration at sunrise and sunset, which may cause flicker. But there is no such rule saying that a Moon duration spell effect should flicker at sunrise andsunset. Quite the opposite, as callen points out. The rules specifically say that the spell effect is maintained throughout the Moon duration (i.e., until the moon rises and sets).
Now, taking a step forward, we can look at what happens when the Maintaining the Demanding Spell effect is put into an item. That might seem to cause you to interpret the effect as flickering at sunrise and sunset, just like a spell effect whose concentration is maintained by a device. But I think that's not the case.
Looking at our first two example, let's see how those would take effect if in a device. If I went to the effort (+3 magnitudes) to make either effect (heat protection or illusion) Moon duration, then they would last for a Moon whether I cast them or invoked them from a device. In each case, the duration of the spell effect is Moon. The source of the spell effect is irrelevant. Each should last until the moon rises and sets without any flicker.
So too with Maintain the Demanding Spell in a device. Once more, it's the spell effect, not the device that's maintaining the spell. And in this case, the spell effect is duration Moon.
Remember, our hypothetical magus has worked up an effect that's two magnitudes higher than Concentration. Even counting the +5 for the device maintaining the concentration, the Moon effect is still a full magnitude higher than the Concentration effect. It ought to be better; it took more effort to create.
In any case, that's my interpretation.