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Updated answer: No, this is not possible with cryptography. You have the ciphertext and you have the key. For all anyone knows, you could have made a copy of those to some other computer and decrypted the ciphertext without telling anyone. There's no way (with cryptography) to prove you haven't done that. One approach would be to implement a secure service ...

It is possible for Bob and Alice to store many files on some host file server using a host-proof protocol -- i.e., in such a way that even the sysadmins of that server cannot decrypt and read the plaintext of those files. You may be interested in browsing the questions with the host-proof tag. As far as I know, there is only one way to prove that those ...

Time stamps are also signatures; see for instance RFC 3161 which is the most commonly used time stamp format. In particular, such time stamps also rely on certificates (the TSA certificate), and thus also expire. So you need regular time stamping; whenever the latest time stamp is about to expire (but before expiration), you need to obtain a new time stamp ...

It would seem that the answer is no. If the TSA's private key is compromised (and thus revoked), the time stamp signature cannot be trusted as whoever compromised it could sign documents with old time stamps. Surely users would want to be warned before accepting a time stamp signature from a compromised certificate. It seems then if this is your threat ...