Unless I’m wrong, the way the plugin is working is to listen any post event, and when it happens, it marks the concerned Wordpress Post to pull the latest comments from Discourse the next time the Post content is loaded.
The immediate issue I could see is you might hit the rate limit for the current API user.
Is the API user an admin? (it has generally less restrictions)
It looks like you are using the normal rates limits.
Here the current limits: Global rate limits and throttling in Discourse
You might need to increase those limits.
Check User API rate limits or Admin API rate limits