When our E1120 controller is offline the APs configured on it stop working. I found that the Poll Timeout setting found in the Device Group and individual AP settings can be set as high as 600 seconds. That helps, a bit.
In our old controller (A C35 running 10.x software) there is an option under the AP Advanced settings named "Maintain client sessions in event of poll failure". It would prevent the APs from failing no matter how long the controller was down. Is the same behavior available on our E1120 controller?
