If by "time based key", you mean the six- to eight-digit one-time password that the user enters, then no, compromising one of those does not compromise future passwords. That's because the one-time password is generated from an HMAC output with the shared secret as the key and the timestamp as the value. If an attacker could determine the shared secret or other outputs from a set of known outputs, then HMAC would not be a secure message authentication code, and we currently believe that it is.
Moreover, the one-time password is derived from only four of those bytes, so even if HMAC with the given hash function were found to be insecure, the TOTP construction is designed to add some additional resistance to attack in the way it selects bytes. However, as mentioned above, we have no reason to believe that HMAC with SHA-1, SHA-256, or SHA-512 (which are the constructions used in TOTP) are vulnerable to a better attack than brute force when used in this way.
If by "time based key", you mean the shared secret (usually embedded in the scanned QR code) that is used to derive the one-time password, then yes, that's a full compromise, since that's the entire shared secret, and it's possible to derive all past and future outputs from that.
