Regarding TCP timeout

RE "So can this be possible that once idle time at LTM reaches, LTM deletes the connection while the server side connection remains open since we have idle timeout configured at server side is 1 hour?":

Yes, this is possible, but the behaviour is dependent on the settings of your TCP profile. If you have reset on timeout enabled, the BigIP will send a TCP reset for the idling connection out to the server once this timeout is reached, pretending it was the client which sent the reset. This should cause the TCP stack of the server to also delete the connection. If you have reset on timeout disabled, you might experience the situation you describe, resulting in a still open connection on the server without according connection entry on the BigIP.