An argument can be made that at some point a wiki will reach a critical mass where it will become self-sustaining. For instance, consider Wikipedia: even though new information is being added and existing information edited all the time, there is really no more need to promote Wikipedia. In fact, growth in the number of people who contribute to this online encyclopedia has almost flat-lined. That is, while there may be different individual contributors over a given stretch of time, the actual overall number of contributors is fairly constant.
With most wikis the growth in the number of contributors in the early days may be slow, but as awareness increases you should expect to see a sudden upward trend. The most common case is to see a spike in contributor numbers and activity around the time of educational events, for example wiki training. However, the underlying trend through these spikes will still be one of steady growth.
After a period of time growth will slow down, especially as the wiki reaches its critical mass of information (or if it’s a wiki designed to support a specific project, as the project nears completion). The growth may even flat-line, although as with Wikipedia, you may still be attracting new contributors.
However, by definition a wiki is never really finished. There is nearly always something else that can be added. Ideally, even at the “critical mass” stage, there will continue to be a slow incremental level of activity.
Keeping the activity level going requires effort. Don’t ignore a wiki just because you feel it has reached critical mass. Once a wiki stops being updated, it will quickly lose its relevance and start to be ignored.
Most of the above applies to the sort of wiki that is intended to be a knowledge base or intranet. There are other types of wiki, such as those used for a specific collaborative project (e.g., editing this book) or to plan a specific event. If you don’t expect the wiki to grow after a certain date, either in terms of number of contributors or in terms of new content, then you’ll need to consider whether to keep the wiki online as an ongoing reference or for historical interest. This may be worth doing, even if there are no resources to “grow” it any further.