In practice, robust mostly comes down to valid, well-formed HTML and correct use of ARIA: unique IDs, properly nested elements, and interface components (like custom dropdowns or tabs built with JavaScript) that expose their name, role, and state to assistive technology, not just their visual appearance.
Because browsers and screen readers are updated independently and frequently, robust code that follows the HTML and ARIA specifications correctly tends to keep working across updates, while code that relies on a specific browser’s quirky behavior tends to break.