These suits allow to survive for weeks out in the deep desert, by catching and recycling all of the body's lost water. Making sure no perspiration can escape is doable. Filtering the sweat to produce clean, salt-free water should be possible as well - membranes for water desalination do already exist today. To have all the required pumping action provided through walking and breathing is a mechanical problem that should be theoretically solvable. The big, unsolved problem I see, is heat.
The book says that the suit's layers closest to the skin allow the sweat to evaporate and thus provide cooling to the body. But the water then has to condensate again somewhere. From my (limited) understanding of the laws of thermodynamics, the amount of extra heat created through condensation, should be exactly equal to the amount of cooling the evaporation provides making the whole cycle a zero-sum affair. But for this cycle to work in the first place, the skin would have to be of higher temperature then the layer where the condensation occurs. If the desert heat is above body temperature, we'd need some sort of heat pump like in a fridge. Using changes in pressure and density (through a compressor) you could cool the suits' inside below body temperature, while heating the outside above ambient temperature - which is necessary to actually give off heat to the outside.
Those compressors are heavy and powerhungry though, and you'd need additional high pressure water lines through the suit - increasing the bulk of the whole thing considerably. Future technology might be more miniaturized and more energy efficient, but still... Maybe piezoelectric/thermoelectric cooling (exploiting the Peltier effect) would be a better choice for a suit like this. Then you'd have a light inner layer that allows for air circulation - so that the sweat can evaporate on the skin, and condensate again at the thermoelectrically cooled middle layer - where it's collected and pumped away to the membrane filters and catchpockets.
The outer layer of the suits would have to be made of flexible solar cells, in order to provide the electricy required for the cooling of the middle layer. Not sure if that could work though. Those solar cells produce a lot of heat on their own, and they sit right on top of the heat-producing side of the thermoelectric cooling. And the sun burning down on it as well - that's a lot of heat right there at the outer layer. I don't think thermoelectric cooling can overcome that high a temperature difference. It works best, when the temperature difference between the cool side and warm side is pretty small.
