As promised, I'll attempt to answer my own question. I'm pleasantly surprised that to date, comments and answers amount to "why would you move (unless you want to)?". This is clearly a very sensible answer, yet it doesn't accord with my own experience of academic career advice (hence the original question). It would be interesting to know whether other people have also gained the impression that "it's important to move around as a postdoc" - perhaps this is field- or region-dependent?
It seems (@PeteL.Clark) that the implied meaning of "postdoc" is also not necessarily uniform across all fields. I'm focussing here on postdocs who are supported by funds secured by their PI, and who are therefore expected to work (predominantly) on a given research project. To my knowledge, this is the most common form of "postdoc" in (at least) the sciences.
As @suresh observed, "the whole point of a postdoc is to transition into some kind of permanent job". So, why would you quit one postdoc for another? For completeness, let's start with the most obvious reasons, which I deliberately tried to exclude when constructing this question:
- The funding for your current position has been exhausted;
- You are offered a position that is clearly a 'step up', academically, from your current position;
- You are offered a position that offers something that is sufficiently attractive to you personally to justify the move (e.g. closer to family, nicer living environment, better pay, etc etc).
What are the other potential benefits associated with moving? Possibilities include
- Exposure to new people, new ideas, new ways of doing things - not everyone approaches research in the same way, and not every department is organised along the same lines: it's good to see some different perspectives;
- Experience of different research questions - the research focus of the new postdoc is unlikely to be identical to that of your current position;
- "A change is as good as a rest" - a move can provide practical and intellectual stimulation, and may lead to a boost in productivity (particularly if it allows you to shake off additional responsibilities for a time);
- It raises your profile in the wider academic community - humans are conditioned to pay more attention to changes than to continuity;
- You get to remind a range of influential people (your referees; research groups that you apply to) that you exist, have attractive qualities, and are in the job market.
Potential downsides might include
- Lost time - the process of winding down your research in one place, transporting your entire life to a different city/country, and getting set up for research in the new place will probably severely reduce your output over several months;
- Dealing with all the hassles (and, potentially, the expense) of relocation;
- You effectively remove yourself from the job market for a time - realistically, you are not going to be able to move again for a while, even if a better position comes along;
- Signalling of limited ambition - people may question why you are taking another postdoc and not concentrating on obtaining a personal research grant/a faculty position;
- Reduced opportunity to benefit from the work you've already done - if, say, your research group has spent the last decade getting to the point of sending a rover to Mars, it is probably not a sensible career move to leave a month before it lands.
There are also various factors which may be either positive or negative, depending upon the precise circumstances in which you find yourself: the relative strengths and weaknesses of the two research groups in question; the personalities involved; and so forth.
Given that the single biggest factor against moving is the time cost, it seems plausible to argue that there is a "minimum length" for a postdoc to be truly profitable. I suggest this is of the order of 2-3 years. Thus, all else being equal, there is limited benefit to moving until you've spent at least 3 years in your present position. There is also little benefit to moving if you can reasonably expect to secure a clear "promotion" (e.g. a personal research grant or faculty position) within the next 2 years.
On this analysis, there is perhaps a short window in the middle of one's "postdoc years" where a sideways move can make sense. This is where the different classes of institution come into play. If, during this window, you can move to an entirely new first-class institution, then you should do so: the benefits are likely to outweigh the losses. However, moving to an institution you have already had an association with is less valuable, as you have already gained most of the "new experiences" that such a move might otherwise provide. A move from a first-tier to a second-tier institution is unlikely to be sensible, unless you can identify specific exceptional circumstances.