Currently SendGridClient support short-lived HttpClient instances using IHttpClientFactory. If not using that, it will internally create a singleton client.
This internal client does not have any configured PooledConnectionLifetime and as a result suffers from DNS errors when a IP adress no longer responds to api.sendgrid.com.
To use the SDK safetly in long running scenarios without ASP.NET Core Dependency Injection - PooledConnectionLifetime should be configured to match the TTL of api.sendgrid.com. From what I can tell with nslookup, that is 60 seconds.