We have noticed multiple times that the connectors could stop working and show as broken when there are changes in the source system that either change the certificates or invalidate the auth token. In some situations these are genuine failures but in many other situations these are just temporary outage caused by server restarts or patches applied at the source system we really don't have control over.

We have also noticed that in the second scenario a simple 'test connector' is often enough to heal and restore it. 

For this reason the feature I would like to suggest is to simply and automatically test the connector if it breaks. The test-connector API parameters could be set at the connector creation time if and only if the user wants to enable it and automatically trust the new connection.