Despite it taking almost a month for me to get around to this. Session management and logins on WikiApiary are fixed.[1]
We're still in the process of moving WikiApiary from Linode to the Wikimedia Cloud Services[2]. The intern who is working on this is in the middle of finals, but should be able to complete it soon after.
When that happens, more people will be able to kick the server than just me.
Thank you for your patience,
Mark.
Footnotes: [1] https://phabricator.wikimedia.org/T191004
[2] https://wikitech.wikimedia.org/wiki/Help:Cloud_Services_Introduction