The short answer, I think, is that no one knows, but that wouldn't make an interesting blog post.
Now, to the long answer...
Over the Christmas period I went out with some orchid friends to pay our respects to the Yellow Hyacinth Orchid which must surely be one of the most difficult orchids to see in the ACT. Paradoxically, it is quite an easy orchid to find as it stands up to 80 cm tall with many large, yellow, spotted flowers. The difficulty comes from there only being one or two individuals in the whole of the territory.
The two individuals were first discovered near Tidbinbilla in 1966 by Ray Nash. I don't know how often it was seen in those early years, but apparently one was seen relatively regularly during the 1980s and 1990s and was last seen in 2002. I believe last year was the first time one had flowered since the January 2003 bushfires.
Back to the question - how long do orchids live? From what I understand from people who've seen it previously, there are probably only two individuals involved, and these are likely the same individuals stretching back all those years. Over 50 years, in fact.
There is little scientific literature on how long individual orchids live. It seems like a major oversight not to know basic information such as how long these things live, but it's actually very hard to measure. Most terrestrial orchids flower each year from an underground tuber, and die back completely over summer such that there is no above ground leaves or stems. Some years when conditions are not suitable the orchids may lie dormant and not produce any signs of life above ground. Predictably, its hard to measure something that you can't see for a third of the year or might not see again for several years.
In many orchids there is also the problem of how you define an individual. In the case of most Australian terrestrial orchids, the underground tuber can be considered the individual. But in some species of Caladenia orchids, a new 'daughter' tuber is grown each year and then the original 'mother' tuber dies off. In this case, the individual is somewhat ephemeral as it is replaced each year by a new tuber. The tubers are produced through asexual reproduction (cloning) so its the same genetic material. Alternatively, you could say that the individual dies each year and is replaced each year by a genetically identical daughter individual. Other orchids, including some species of Pterostylis, multiply clonally by producing 3 or more tubers each year. Each tuber then goes on to produce 3 more, and very quickly you can end up with 1000s of tubers. The genetic material is the same, so in a way they are the same individual, but in some cases it may make more sense to think of each tuber as a separate unit.
Oddly enough, the largest and oldest organism in the world is sometimes considered to be the quaking aspen (Populus tremuloides). There is a clonal colony of male trees in Utah which covers 107 acres, has around 47,000 stems, and is estimated to weigh 6000 tonnes. The individual stems are continually being replaced by roots beneath the ground. Its hard to know how old this clone is, but estimates suggest 80,000 years or more, conceivably as many as 1 million years old.
Back to the orchids, one study on Cypripedium calceolus from Poland which suggested that the lifespan of 'clumps' of orchid roots was estimated to be around 25 to 100 years and possibly 300 years or more. Similarly, genetic data from clonal Chiloglottis orchids in eastern Australia suggested that clones were likely hundreds, if not thousands, of years old. On the other hand, some terrestrial orchids are quite short lived, for example Coeloglossum viride in the Netherlands has a half-life (the time it takes for a cohort of plants to decline to half its original size) of only 1.5 years. Similar for Ophrys sphegodes (mean half-life of 1.9 years), although the related Ophrys apifera lives longer, with a mean half-life of 6.6 years. Longer lived European orchid species include Dactylorchis sambucina and Listera ovata (mean half-life of 20 and 80 years respectively).
In general, shorter-lived orchid species tend to be able to flower quicker, produce more seed, and are perhaps less likely to remain dormant, while longer-lived species require several years post-emergence to build up the carbohydrate reserves to be able to flower, and may be more likely to remain dormant below-ground in unfavourable years.
Given the variability between different orchid species, it is hard to know exactly how long orchids live, but I would hazard a guess that the lifespan of many of our terrestrial orchids would be measured in decades, not years. The yellow hyacinth orchid we saw flowering last year may well be the same individual that flowered in 1966.
Mitton, J., & Grant, M. (1996). Genetic Variation and the Natural History of Quaking Aspen. BioScience, 46(1), 25-31. doi:10.2307/1312652
Nicole, F., Brzosko, E. and Till-Bottraud, I. (2005). Population viability analysis of Cypripedium calceolus in a protected area: longevity, stability and persistence. Journal of Ecology, 93: 716–726. doi:10.1111/j.1365-2745.2005.01010.x
Willems, J. H., & Melser, C. (1998). Population dynamics and life-history of Coeloglossum viride (L.) Hartm.: an endangered orchid species in The Netherlands. Botanical Journal of the Linnean Society, 126 (1-2), 83-93.