I googled around a little and read that an average human being needs at least 1 litre of fluids (water) per day to survive, ignoring other factors such as heat or activity causing perspiration. If I remember the mechanic and calculated correctly a player should roll on average 18 times for a resource to go empty from a D12 (D12 → D10 → D8 → D6 → 0), meaning a D12 is at least 18 litres of water, probably more... that's a lot of water to carry around in your water skin.
Suggestions so far are very good, and I will probably implement the first two, like you can see below.
Changing the mechanic, as suggested, from (1, 2) to (1, 2, 3) lowers the average rolls by 1/3, so D12 → 0 equals around 12 instead of 18 rolls. These amounts work quite well with food, arrows and torches too I think to keep the rules consistent for all resources. Increasing encumbrance on water and possibly food, makes transporting larger quantities of these more difficult too.
I have also house ruled that when you roll a 1 or 2 (now including 3) on the D6 resource die, the character discovers that they are running very low on that resource. There is still one unit left (D12 → D10 → D8 → D6 → 1 → 0). This makes running out completely of a resource less of a surprise; you'd think that the character would notice and think to themself "I'm running very low on water, but I'll get by until tomorrow!" instead of being completely left without.
D6 (~2 units)
D8 (~5 units)
D10 (~8 units) heavy (2)
D12 (~12 units) heavy + normal (3)
(All average units in above table is +1 if you use my house rule of D6 → 1 → 0)
Another idea to consider if you want to "keep it simple, stupid!" is to just increase the frequency for which you roll your water resource die. For example additional rolls, due to manual labour (such as hiking) and possibly for weather or other external influences too.
Or just add that as well to any other changes you make if you want to torture your players and their characters........