A "503 error in heartbeat manager" or "Service returned a 503, marking the collector as offline" is a response message from the Sumo Logic service that lets the Collector know that the service is currently not available to process the message request. When this occurs, the log messages that were attempting to be sent, are stored in the Collector cache. They are then re-sent as part of the next request to the service.
This is typically a temporary condition. If this error continues to occur for an extended period of time, please check the http://status.sumologic.com/ status page for documentation on any service related issues.