The magic-link re-sync sends a fresh push of all your property data from HomeRunner’s servers to your WordPress site. When it fails, the problem is usually that the delivery path from HomeRunner’s servers to your site is blocked. It does not mean anything is wrong with your PMS connection.
Why this happens. Common causes are a firewall or CDN (such as Cloudflare) that rejects the incoming requests, or an SSL mismatch between your CDN and your hosting provider.
What you can do. Contact support. Support can check the delivery logs to identify exactly where the block is occurring.