I have tested this with a new site hosted on WP Engine. I believe your site is hosted there as well. With the default WP Engine caching enabled, I’m not having any problems logging into the site via Discourse.
Are you using Cloudflare? If so, I suspect the problem is related to what is described here: https://meta.discourse.org/t/wordpress-sso-expired-nonce/105159/14. Would you be able to give some details about how you have Cloudflare configured?