A job which initiates a transition in Jira via the "Progress issues by workflow action" post-build step will succeed if the job is located in the Jenkins root.  If that exact same job, however, is relocated to a sub-folder (per the Folders plugin), it will always fail with:

• a "[JIRA] Failed to connect to JIRA" error in the build log
• a "JIRA session could not be established" error in the plugin's JiraSite class

I've reduced the scenario to the most basic configuration I could and validated that the only variable between a successful run and a failed one is the location of the job relative to the Jenkins root.  It appears, just on cursory inspection of the plugin's code, that the Jira credentials are "missing" when the build is run from within a Jenkins folder.

Attached is the affected job's configuration.