I am using Ruckus ZD1100. I have setted inactivity time out as 240 mins and grace time as 30 mins.
Still I am receiving complaints from my students as they are logged out in every few minutes. I have to prove that they are connected upto 240 mins. So I need to know the connected user start time and disconnected time.
Log which you are showing indicates that user was kicked out from WLAN as they failed to authenticate correctly or there was a delay in entering authentication details.
I also noticed that you hit the bug - ER-1553 and i am sure that you have upgraded to latest 9.8 firmware and if you are still seeing the issue then good time to report the issue to Support.
As far as answering your question: - you can setup a syslog server then whenever any user connects to that WLAN - you can see the log which shows starts time and then you can track down on disconnected time. i know this is little rough but can be effective as you can do quick search on mac address, track repeat disconnects and keep them for record too
This is a generic log. To really find out whether "user was kicked out by AP" or "user went away on its own", you will have to take Over the air wireless capture as it will tell whether decision to exit(deauth or disassoc) came from AP or STA(user).
You can use packet capture feature on the ZD/AP to achieve this.Refer to KBA on support site to take this further.