You can check the /var/log/ltm* log files to see when the state changed. I don't think this type of info is accessible anywhere else by default. If you want to check for more than 8 days you can either modify the logrotate configuration (see man logrotate for details) or send the logs to a remote monitoring station using a custom syslog configuration.
I thought there would some config setting which would show the timestamp of the change in b node/pool show command output itself. It looks like ltm* files and/or an external syslog server are the ways to look for the information.