At what point should an early team stop shipping features and fix messy code?

We spent four straight months pushing out user-requested features as fast as possible to beat competitors. It worked for initial traction, but our codebase eventually turned into a fragile mess where adding one simple toggle broke two unrelated workflows. We had to freeze all new releases for three weeks just to refactor core modules and set up proper automated tests. It temporarily stalled our roadmap, but our error logs dropped by 80% and long-term development speed doubled afterward.

​How do you convince stakeholders that spending time on internal code refactoring is more valuable than pushing out shiny new features?