There tends to be an all-or-nothing approach driven into our heads about web redesigns – either you redesign the whole thing, or you don't.
These are just a few of the questions that can determine whether your site needs to be scrapped, or if ongoing optimization would be a better route.
Radical redesigns are risky. Redesigns often change page structure, URLs (which need to be redirected), content, layout and design. They are not truly based on data since dramatic design decisions are often made that cannot be tested and are instead based on the designer's intuition. Besides having SEO and traffic impacts, these dramatic decisions can affect conversion rates, or how often users on your site perform valuable activities, such as filling out the contact form, clicking on the "buy" button on a product, eCommerce check-out, donating, etc.
A radical redesign is better when:
Digital Impact Optimization, an evolutionary model, is a better route to follow whenever possible. Don't let yourself be sold into a redesign just because you're frustrated – sometimes, there is hope for the current site, and its very existence, analytics and traffic are more valuable than you think.