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have you been able to recover a page from panda or penguin by a simple URL change on the same domain?
"I heard of several Panda recoveries that followed on URL changes - but the recoveries were short lived and they disappeared after the next Panda Update."
Sometimes people use the word "URL" and the word "domain name" to mean the same thing.
does any one have GA installed on these domains?
It may be that you've too obviously targeted your deep page and Google is aware of the manipulation, so Google is pushing the page down.