Likely this is result of check_admin_referer() function not recognizing your request as coming from admin area. Since your query clearly contains nonce it is likely what is not being recognized.
Nonces can be locked down in many ways. They are unique to the WordPress install, to the WordPress user, to the action, to the object of the action, and to the time of the action (24 hour window). That means that if any of these things changes, the nonce is invalid. ( Mark Jaquith )
My theory is that your load-balanced installs don’t count as same install for the purpose of generating nonce. If possible try to limit admin area to single server and see if that helps.