Did you increase the "Inactivity Timeout" in the advanced options? It should say Terminate idle user session after 5 minutes of inactivity after creating your WLAN. You can change to a Max of 500 minutes. Not sure if it can be disabled in CLI or not.
This behavior is a result of current iOS software's aggressive power-saving strategy.
Current iOS devices will typically disassociate from their AP shortly after their screen has been deactivated. They will periodically wake up, re-associate, check for pending application-layer notifications, disassociate, and repeat the process. They will re-associate as soon as the screen is activated and will stay associated for the duration of screen activity.