You could add an iRule to the HTTP(S) and LDAP VIPs to log the connections or you could run tcpdump. Once you have an idea of the traffic flow, you could troubleshoot the slowness in the websphere connections being re-load balanced to a new member.
If you have a monitor configured on the pool and a member goes down, you can configure LTM to send a TCP reset or reselect a new pool member. By default nothing is done, so the TCP connection would just time out. You can configure this behavior on the pool using the 'action on service down' option. Note that there was an issue with the reselect option in some versions (SOL8160
Click here).
Aaron