I would try to consider the architecture of the system and see whether it is possible to scrap and rewrite specific well defined components without starting everything from scratch.
What would usually happen is that you can either do that (and then sell that to the customer/management), or that you find out that the code is such a horrible and tangled mess that you become even more convinced that you need a rewrite and have more convincing arguments for it (including: "if we engineer it right, we would never need to scrap the whole thing and do a third rewrite).
Slow maintenance would eventually cause that architectural drift that would make a rewrite more expensive later.
