Check out this interesting article about the reanimation of an orphaned plant database and its associated ArcIMS instance. The analysis of the issues is sound. I disagree, of course, with their conclusion that ArcIMS is something worth learning and deploying in 2008, and this raises in my mind another issue that the authors did not identify: is not the project's data and its provenance the thing that is most important to preserve? Must the interface cruft around it be preserved in anything other than an archived form, if at all? The ArcIMS user interface and the species database browser are no kind of programmable web APIs; it's unlikely any other application would be broken by a switch to some free web mapping framework or modern search interface.
Now there's a question: switch to what? If this story is just the beginning, and bigger boxes of used, discarded, but potentially useful first-generation web/GIS projects end up in the laps of librarians, a turnkey (and open source, naturally) ArcIMS to MapServer/MapGuide migration tool might be a handy thing. I wouldn't be surprised if such a thing existed. Its authors might want to consider pitching it to GIS librarians in higher education.