What is her diet like? Maybe if we knew would could better tell you whether or not she is drinking too much water.
Personally, to me (I have 5 pigs) none of them could drink close to that in one day. My 5 pigs go through about 15oz of water TOTAL (that's about 3oz a pig) a day. They also get unlimited timothy hay, 10oz of pellets a day, lots of leafy greens (which I wash and pat dry) that a a little damp, and various other vegetables with the occasional piece of fruit.
So I would say 16oz PER a pig in a day is too much.
The following link is taken from guinealynx,
(broken link removed)
It states that a symptom of diabetes is excessive thirst.