Problem:Eye-Fi center doesn’t appear when I click on it in the tool tray, following an upgrade.
Eye-Fi answer:

Your request (#27954) has been deemed solved.
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Michal, Apr-20 05:25 (PDT):
Hello Adrian,
As discussed could you please do the following:
– format the card in your camera
– uninstall Eye-Fi software as well as Adobe AIR
– install the latest version of the Adobe AIR from the following link:
http://get.adobe.com/air/
– download and install the latest version of the Eye-Fi software:
http://support.eye.fi/support-resources/downloads/software/eye-fi-manager-desktop-software/

Please feel free to contact us again if you have questions or would like further assistance.
Kind regards,
Michal
Eye-Fi Customer Care

… or to put it another way, turn it off and turn it back on again!
Sometimes I think that things haven’t really changed since I did support back in the 1990s.

Update:
The correct solution is to uninstall & reinstall Adobe Air.