If one is sitting and drinking water while studying, without moving from the desk, does he have to re-make the shehakol if there passes a certain interval of time which he has not had a sip of water? It seems like a very simple question but the closest other answer I could find in your Q&A database was the case of a woman having made the beracha and then bringing the water into the car with her, but this is obviously a very different scenario and one that would be very relevant to one sitting and learning in a Beit Midrash.
If one is sitting and drinking water (or other drinks), taking a sip now and again while studying, one would not have to make another blessing even if a lengthy period of time goes by. It is normal practice to sip and drink once in a while, and the initial blessing is made with this normal practice in mind, so that the blessing includes the full duration of the study session.
One should be wary to have in mind that the blessing should apply even if one steps out to the toilet (going from room to room, but not entirely outside the building), so that one would not get into doubts concerning making another blessing after coming back.
Sources: This halachah is mentioned in a number of modern-day berachah books. See Vezos Ha-Berachah p. 53.