I think we need a bit more information.
Is each switchport configured the same?
Are your LTM instances allowed to use both blades in each chassis?
Some items to note:
Best practice (and maybe a requirement?) is to have identical network configurations for each blade in a 2400 chassis. It doesn't necessarily matter what switch your are connecting to, but as long as the number of connections is the same and the port configuration is the same to each blade.
The backplane is for supplying power, it is not designed to pass traffic. The design is to use the network for everything; even failover.
If you're LTM instances are not configured to use both blades there is no automatic transfer in the event of a failure. Your HA should be between the chassis, with the possible addition to having your LTM instance use multiple blades in a chassis.