Ask three questions about your current site, in order.
First: is the story right? Show your homepage to someone who matches your ICP but has never seen your product. If they can say what you do, who it's for, and why it's credible within a minute, your positioning is landing. If they can't — and the reason is that your actual positioning has changed since the site was built — you have a redesign problem. If they can't because the page is cluttered or vague, that's iteration.
Second: where does the data say people leave? If drop-off concentrates at specific points — pricing, signup, a particular step in the flow — you have identifiable leaks, and leaks are iteration work. If engagement is weak everywhere, uniformly, the problem is more likely foundational.
Third: what's actually changed in your business? A rebrand, a pivot, a new primary persona, a move upmarket — these justify a rebuild. "The site feels old" and "the CEO is bored of it" do not. Aged aesthetics can usually be refreshed within the existing structure at a fraction of the cost.
Most teams who run this honestly land in the same place: the story is roughly right, the execution leaks, and what they need is a sustained run of focused iteration — not a six-month rebuild.
And if you genuinely do need a redesign, iteration is still how you protect it. The teams whose redesigns actually pay off treat launch as the starting line, not the finish. They rebuild the foundation, then keep improving on top of it every month. A redesign without iteration behind it starts aging the day it ships.