I just realized that all nonces now get updated when the preview refreshes as of #35617, making this ticket less important. This ticket now specifically fix the issue where the Customizer is left open for a long time without the preview being refreshed to keep the nonces up to date. Nevertheless, if the user does leave the browser session open for such a long time, it is also likely that their session will expire and they will need to re-login anyway: by default, non-remember user authentication sessions expire after 48 hours (auth_cookie_expiration) and nonces expire after 24 hours (nonce_life).
Nevertheless, the integration of Heartbeat into the Customizer will be useful for plugins generally, so I'd love to see that happen, and keeping nonces up-to-date should be the first application of Heartbeat in the Customizer. That can either be made the scope of this ticket, or another ticket can be made specific for that feature.