The SiteMonitor plugin voids cookies that are held by other plugins.

For example, using the VSphere plugin and SiteMonitor plugin on the same system, everything works fine for the VSphere plugin (logins, actions on VSphere). However, after the SiteMonitor plugin runs, the VSphere plugin can no longer establish connections to external systems, because the cookies are invalid.

Particularly, this code in SiteMonitor is where the damage is being done:
https://github.com/jenkinsci/sitemonitor-plugin/search?utf8=%E2%9C%93&q=CookieHandler

As you can see, sitemonitor checks to see for a null CookieHandler and then sets its own. This caused the override and the empty cookies...