Visit my.sonatype.com for documentation on Nexus Repository version 2.
The uptime of a Nexus Repository 2 instance can be monitored by using the /service/local/status REST resource, e.g.:
The current state of the server can be found in the "state" field of the response, and the start time can be found in the "initializedAt" field.
You can use this REST endpoint in conjunction with your whatever server monitoring you have in place, and have it raise an alert if the resource either fails to respond, the "state" is not "STARTED", or the "initializedAt" field contains an unexpected time.