Nimbostratus
Cirrostratus
It would help to identify what's different when you're testing through LTM compared with direct to the application. Are you offloading SSL on LTM and using cleartext to the pool member? Are the VIP and pool member defined on different ports?
You can use a browser plugin like HttpFox for Firefox or Fiddler for IE to record the HTTP requests and responses when it's failing through LTM. If the issue is not readily apparent you can compare the failure scenario with the working logs taken on tests direct to the application.
Aaron