The logic doesn't make sense. If they ran out of water and don't find more after traveling 1 day deeper, then I don't think they could travel 1 day back, and then the rest of the way to the beginning, and then climb back up all without water.
@Nk9bjP4A
The uncle has become very obsessed and frighteningly driven by his beliefs, while also abandoning any logical reasoning. The nephew isn't thinking clearly either, underestimating the effect of having to travel 24 hours (and more) without water while also being dehydrated... If they decided to travel up again they could restock on water. Also with enough funds, they could hire more people and might even be able to create a working supply chain of food and water, if the uncle wasn't so secretive about the discovery...
Of course it could also be that the mangaka didn't really consider that the 1 day more plan in reality would end up lasting much more than 24 hours when travelling forth and then back again.