If adversary has all versions, is deniability of hidden data still posiible?

If adversary has repeated access to a truecrypt container in cloud storage, ie several versions where the hidden data change, they can prove the existence of the hidden data.

Is this because of the design of truecrypt, or an inevitable fact of all deniable encryption?

What if the keys change from version to version? Automatically based on random movements of the mouse? While the password stays the same? Is hidden data deniable then?