A technical question: which is easier to build an LH2 depot at, a low Earth orbit well below the Van Allen belt inner layer (and also more easily accessed from Earth) or a high orbit?
In a high orbit, such as the Lagrange points, the depot is continually exposed to sunlight. That may be no bad thing, if the depot can orient itself so one face of it always is turned to the Sun--the Sun is probably the power source for any active recondensing that might be going on, and anyway you concentrate all the heat shielding on that vector. But the Sunlight never goes away.
In LEO on the other hand, Earth looms, taking up nearly half the entire sky. This means that almost half the time the depot is in shadow as far as the Sun is concerned, and that would seem to cut the basic problem just about in half.
However, Earth itself is no mean source of infrared radiation. (A secondary technical question--I have the impression that simply reflecting infrared is a bugger of a design task--we can reflect 90 percent or more of light in the visible spectrum, and I'd guess do about as well with UV, but below a certain transition level--I'd guess the level where the wavelengths correspond to molecular-scale excitations of whole molecules rather than quantum-jumping of electrons in atomic shells--everything becomes pretty much "black;" just about every substance absorbs all the IR and reradiates it. No "white" substances for IR--true or false?)
The real bugger of Terran IR radiation will be during the day, when the satellite is also exposed to the Sun. Presumably the main heat shielding is again oriented to block the sunlight, but that leaves Earthlight reflecting on it unimpeded.
I would guess the Earth's IR output is more intense on the day side, but also that even at night it maintains almost daylight levels--that is, little IR is reflected, most of it is reradiated, and not from objects on the surface that get hot in the day but cool down at night--basically from some broad strata in the upper atmosphere that stay at pretty much a constant temperature.
Thus the LEO version gets the direct sunlight cut in half, which is good, but is constantly exposed to dim but continual Terran IR, which is bad. Especially because the Sun is a highly concentrated source but Earth sprawls over half the sky.
We could have a secondary heat shield and it should be possible to maintain the craft's attitude to block both, the thing rotating around its sunward axis which slowly precesses over a year, at a 24 hour rate that has the secondary on the bearing it needs to be.
Still, during the day, where will an actively-recondensing depot radiate its waste heat? At "noon" when the satellite is poised over the vector connecting the Sun to Earth, half its sky is blocked by the Earth IR shield, and the other half is dominated by the Sun. Pretty tricky!
It all depends on the sorts of pressures and temperatures an active recondensing system can achieve--with radiators good and hot it won't matter then that they are exposed to backflow from one source or the other, not much anyway. With them operating with great delicacy on very slow, gentle gradients, that factor might matter a whole lot.
And I do realize you haven't yet described an active one that can maintain a given stock of LH2 forever by constantly recondensing the inevitable boiloff--just ingenious systems to slow that rate down so losses are low after long time periods, presumably longer times than it takes Earth to replace the lost hydrogen. For such a passive system the whole name of the game would be to simply shroud the tanks as much as possible, and accept that some boiloff is going to happen anyway.
It seems to me other things being equal, high orbit is clearly superior, offering the depot pretty much constant conditions to be optimized for and a relatively simple environment.
But obviously other things are not equal:
1) High orbit means it is expensive to deliver a given mass there, including the eventual mission craft that want to tap the fuel;
2) High orbits are in the radiation belts, which are a hazard for any manned missions and will cause deterioration and unreliability of whatever electronics the depot does need;
3) Most high orbits are not "on the way" to likely destinations--obviously a few are, such as the Lagrange points. (They also don't suffer from Van Allen Belt concentrated radiation, just constant cosmic rays and the unshielded Solar wind). But these favored locations are very far from Earth indeed.
If I recall correctly, e of pi once observed that a teacher of his calculated a satellite in low Earth orbit should have little trouble maintaining LOX below boiling--implying that it would be otherwise farther out from Earth, implying that despite the complicating factor of IR coming from the large disk of Earth, the interrupted daylight of the low orbit is the winning factor, leaving it on the whole easier to operate a depot (at least for oxygen) there. I'd think if it's easier for LOX, it is less difficult for hydrogen as well.
So does the properly educated and up-to-date astronautical community have hard and fast, well-established answers to these questions of thermal cosmography, or is it all as yet a matter of a handful of paper projects whose conclusions one takes with grains of salt graduated by industry knowledge of who these people are, how much are they paid to take this stuff seriously, and what do they like to smoke?
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