IAs this expert knows only too well from personal experience, persistent hiccups/hiccoughs can be a very distressing experience, not the increasingly funny experience which many observers seem to find it.
There is a little bit of evidence for the use of acupuncture, mostly in the form of what are called case studies about single instances where treatment has helped, or sometimes where treatment has been offered to a specific target group where hiccups often present and where there is a need to deal with them quickly, as in post myocardial infarctions. Below are a few examples of these kinds of studies
Most practitioners during their training learn a number of what we call 'first aid points' which are known to have an effect on specific conditions. There are certainly two or three which are commonly used to stop hiccups, and one additional one which appears to be effective for treating children with persistent hiccups. Overall, though, there isn't a great weight of evidence, and we would be a little remiss to suggest that acupuncture definitely provided a solution.
However, that said, we are practising a system of medicine where hiccups, a symptom like any other, is not always seen as the problem itself but is usually a manifestation of other imbalances and blockages in the system. As you may have read, Chinese medicine is premised on the understanding of the body as a system of energy in flow, and the skill of the practitioner lies in making sense of symptoms within the general background context against which they appear. This is why the same symptom can often be treated in a dozen different ways in a dozen different patients depending on what internal causes are allowing it to develop.
The short answer to your question is that you may have to visit a BAcC member local to you for them to be able to see what is going on and try to make sense in Chinese medicine terms of what is happening. This is the only way that you will get a clear idea of how treatable the problem is. What we can say, though, is that with conditions like this we tend to take the view that if they are going to respond they will do so quite quickly, and as such we would caution a prospective patient about getting engaged in a long run of treatment with no obvious improvement. We would suggest three or perhaps four treatments would be the maximum we ourselves would offer before reviewing the case in depth and deciding whether there is any point in carrying on.
This all sounds rather negative, especially when many of us have stuck a needle in with almost immediate effect like a party trick. However, everything works for someone, but something doesn't necessarily work for everyone, so we would advise caution.