@rajrathodbvn what you are describing is not the behavior of the plugin. If you have established a connection to your Elasticsearch cluster and the cluster properly responds to /nodes/_plugins requests, and you have at least two nodes as recommended for a production instance by Elastic, there are no warnings shown whatsoever.
I would note that the plugin will automatically fall back to WordPress search if unable to connect to the Elasticsearch cluster, so you won’t necessarily see any errors even if there’s something wrong. If you believe you’re seeing prompts stating you are not connected and you are connected properly, please install the Debug Bar and Debug Bar ElasticPress plugins to confirm your queries are going to Elasticsearch and being properly formatted. If they are, please file a bug report here https://github.com/10up/ElasticPress/issues.