Medical Theory : Hiccups are linked to the need for social attention. (or, Hiccups are an attention seeking device.)
I can't be arsed writing a proper paper so I'm publishing the idea here.
But basically, I propose that as an infant, hiccups are the one thing that gets you adoring attention without you being blamed or accused of doing it on purpose. You hiccup, then everyone goes "ooowww.. isn't that cute". Free attention gained!
In my own research conducted by and on myself, I have found that hiccups are far more difficult to get rid of, until the point of time where someone notices the hiccups. Then I can get rid of them far more easily.
As a life-long hiccupper (or perhaps hiccuppee) I have tried every method to get rid of bouts of hiccups, and although they have worked for a while, eventually that method was no longer effective. I guess the novelty had worn off for spectators. "Oh he's doing that thing again". Attention wane!
The "cures" that are more elaborate and comical or complex and enjoyable for outsiders to witness, are usually the more successful. It has been said (by people, needs citation) that it's because the brain is working hard on the complex task that distracts the body from hiccuping, but I also reckon the added attention from drinking a cup of water upside down, whilst standing on one leg may also help satisfy the human in question and diminish the need to hiccup. Attention gained!
I call upon the medical community to do some research and prove my theory... but in the meantime, remember where you heard it first.
p.s. I googled it once, and there didn't seem to be anyone else claiming this idea...