There is a workaround that may be helpful until the issue gets fixed. In your build script, use the jFlags option to transfer the proxy settings to the javadoc task:

javadoc {
    options.jFlags('-DproxyHost=' + System.properties['http.proxyHost'],
            '-DproxyPort=' + System.properties['http.proxyPort'],
            '-DproxyUser=' + System.properties['http.proxyUser'],
            '-DproxyPassword=' + System.properties['http.proxyPassword']);
}

This assumes that you have specified the proxy settings in your gradle.properties like this:

systemProp.http.proxyHost=host
systemProp.http.proxyPort=port
systemProp.http.proxyUser=username
systemProp.http.proxyPassword=password

proxyUser and proxyPassword can be omitted if the proxy does not require authentication.

As announced on the Gradle blog we are planning to completely migrate issues from JIRA to GitHub.

We intend to prioritize issues that are actionable and impactful while working more closely with the community. Many of our JIRA issues are inactionable or irrelevant. We would like to request your help to ensure we can appropriately prioritize JIRA issues you’ve contributed to.

Please confirm that you still advocate for your JIRA issue before December 10th, 2016 by:

• Checking that your issues contain requisite context, impact, behaviors, and examples as described in our published guidelines.
• Leave a comment on the JIRA issue or open a new GitHub issue confirming that the above is complete.

We look forward to collaborating with you more closely on GitHub. Thank you for your contribution to Gradle!

Thanks again for reporting this issue. We haven't heard back from you after our inquiry from November 15th. We are closing this issue now. Please create an issue on GitHub if you still feel passionate about getting it resolved.