I've been a part of 2 major rewrites and in both cases it was because of a significant technological change. The first was moving a DOS app to Windows. The second was moving a desktop-based VB solution to a web-based .NET solution.
In your situation, since it sounds like you're not changing technology then perhaps you are really talking about some serious "refactoring". With careful planning I suspect you can figure out a way to make the changes a little bit at a time without having to get management to support a "rewrite". In conversations with management instead go with terms like "refactoring", "optimization", "performance improvements", "better maintainability", etc and work to get time scheduled into the normal project cycle for these things.