To put it pithily, when "the problem has moved on from the solution", a rewrite might make sense. What I mean is that the existing software has existed for long

To put it pithily, when "the problem has moved on from the solution", a rewrite might make sense. What I mean is that the existing software has existed for long enough, without incremental upkeep and rework, that the problem it was originally solving has evolved to the point that the existing software is not only inadequate, it's wholly inappropriate. I'm part of one of those rewrites right now, and while it's true that it's taken much longer and had other ancillary issues, it's clear that the problem really has moved on, and there are needs that can't be addressed without a fundamentally different solution. It's kind of trading a hard problem for a harder one: we're forced to really understand the domain we're serving, rather than simply reimplement a set of existing capabilities. (But then, I don't think maintainable, evolvable software can reliably be created without understanding the domain to begin with.)