A hiccup (medically called singultus) is the sudden onset of erratic diaphragmatic and intercostal muscle contraction and immediately followed by laryngeal closure.

They are usually self limiting, but if they last more than 48 hours, it is considered "persistent", and if they last more than 2 months, it is considered "intractable." I personally think 2 HOURS of hiccups should be called intractable because by that point I am ready to go into a padded room.

There is a reflexive neurologic arc that causes hiccups, a daisy chain of communicating nerves so to speak, of connections that propagate a hiccup: It involved the peripheral phrenic nerve that innervates the diaphragm (the membranous muscle that, like a bellow, inflates the lungs), the vagus nerve & sympathetic pathways up to the central midbrain (likely lower brainstem spots as well) and then back down to the diaphragm and intercostal muscles of the chest along the phrenic & accessory nerves respectively.

Anything that adulterates this arc will lead to hiccups, either physically interfering or metabolically interfering with or irritating the communication within this arc. I have personally seen hiccups related to physical impairment such as midbrain stroke or intracranial space occupying lesions otherwise, like hematomas or other tumors, abdominal trauma, and related to suspected herpetic lesions and runaway pulmonary infections, as well as the common gastric reflex or its cousin LPR (laryngopharyngeal reflux) albeit more severe.

Pharmacologically I have seen it related to to medications I prescribe for Parkinson's, and seen it persist peri-operatively in the hospital related to anesthesia.

At a personal level, I get stubborn (not quite persistent) hiccups with the use of even short courses of 5-6 day steroid tapers, which is well established, along with other, more... fierce chemotherapies known for causing hiccups as well.

I cannot imagine a hiccup lasting longer than a day, as I am phenomenally frustrated if my hiccups last longer than 10 minutes, finding it difficult to eat & talk through the hiccups and getting chest pain (costochondritis type) when it keeps going.

Medications to treat hiccups primarily act by reducing irritability of the nerves along this arc or the diaphragmatic muscle itself, so that includes muscle relaxants like baclofen, antiepileptic medications like gabapentin and various benzodiazepines, and medications that may work on the arc more centrally in the brain, like serotonergic medications, prokinetics, chlorpromazine, amantadine. There are other medications which have been tried, but one should know that there ARE medications out there if push comes to shove.

But most of the times they are self-limiting, which has led to a large number of things tried and seemingly effective either because they are effective or just seemed to work because the hiccups were on their way out anyway. I just Googled up a compiled list of someone out there of over 200 home remedies, as varied as inflicting some sort of pain, attempting strong mental distraction/feedback maneuvers, various breath holding trials, singing, applying mechanical pressure somewhere...

After about an hour of strong hiccups, I looked up the lists and started down, trying everything. EVERYTHING. I even neurologically worked through anatomic pathways and tried squirting vinegar intranasally, to stimulate the posterior pharynx to impact nerves that overlap afferent branches of the hiccup reflex via the sympathetics--NOPE, dumb idea, didn't help but wasn't my favorite next 5 minutes with both hiccups and a burning behind my upper face. I eventually found that for me to break the arc, I can be successful with two separate things. Here they are in case they help you:

1) I fill my bathroom sink with hot water. Then I stand there and take the deepest breath to the point of feeling the diaphragm & ribcage stretch and hold it as long as possible (I tried this on its own and it didn't help), and then when I think I absolutely can't hold my breath any longer, I submerge my face in the hot water and then let the air out as slowly as possible and then come up. Sometimes it takes a few tries but usually works. I think this works via the Hering-Breurer inflation reflex which travels along the vagus nerve and may interrupt the hiccup arc in combination with the diving reflex which also acts along the trigeminal nerve to the vagus, and sympathetics, broadly effecting the brain, heart, and lungs to prepare for diving into water without drowning (in this case due to something like hiccuping in water I guess). This diving reflex that helps you not trying breathing underwater is why that famous Nirvana cover isn't being cruel to the baby:

2) The other thing I do is lie down on my back with a paperback and cover my nose and mouth and hyperventilate into it without letting in fresh air, until I start to feel hot and woozy, so I know that my CO2 has risen (hypercapnia). When I do this, I have my head slightly to the side so that if I pass out, the bag will fall off my face and not kill me. I believe this is working along the pulmonary chemoreflex via the respiratory acidosis-triggered vagus nerve directly and slower umyelinated C fibers as well, setting up a broader cascade, these receptors in the carotid artery and aortic arch (sensitive to CO2 & O2), and in the medulla (sensitive to CO2 & pH changes--acidosis related to breathing like this).

I hope one of these may work for you too, although please don't try either of these if your heart is fragile, as I can reason out how either could precipitate a cardiac arrhythmia.

As you can imagine, trying to find the source for some people can be quite difficult given the large variety of potential causes but also due to the long pathway of the various nerves involved from the brain into the abdomen and back again.

This list below represents the broad differential but is itself not specifically exhaustive. 

I hope you are never burdened with regular or stubborn or persistent or intractable hiccups.