I have got the following behavior with the plugin. I have created new influxdb target in Manage Jenkins > Configure System and after that one became available for "Publish build data to InfluxDb target" in my job configuration. But when I have restarted aplication, Jenkins lost all InfluxDb targets in Manage Jenkins > Configure System.

Steps to reproduce the issue

1. clean JENKINS_HOME (rm -rf ~/.jenkins)
2. java -jar jenkins.war (instal jenkins using default configuration)
3. install influxdb plugin via Manage Jenkins > Manage Plugins
4. restart jenkins (<jenkins_url>/restart)
5. go to Manage Jenkins > Configure System, create influxdb target and click Save. The target is available for Freestyle project.
6. restart jenkins (<jenkins_url>/restart)
7. go to Manage Jenkins > Configure System. Influxdb target configuration is unavailable.