I'd emphasize that failure on a project like this may not be what you'd traditionally have in mind when thinking 'that project failed', though it happens and it could be that bad in the absolute worst case.

The issue is primarily that of the reward versus cost -- especially the opportunity cost.

When the system is rewritten, will the business have increased revenue or decreased cost? Will it do so significantly, surpassing at least the cost to rewrite (salaries, etc) -- that's the absolute minimum bar, but then you have to consider the opportunity cost which is the real concern:

If you had instead spent the same amount time adding new features, implementing an A/B test suite to increase conversions, improving marketing capabilities, retention mailers, or really any other activity that could positively impact the company business metrics -- would the impact be better than the impact of the rewrite?

In most cases the customers (internal or external) don't really know or care how good/bad the underlying code is, as long as the product serves their needs. When that's true, even partially, the value of 'rewrite' almost never exceeds the opportunity cost alone, let alone the absolute cost (and that's to say nothing of the risks).