Is it possible to construct a passively self-destructing message?

Let's dispense with the "if it can be copied" part first. I can start with a camera and work my way down from there. I can also enlist a sufficient number of monks, nevermind digital media.

You're on a track with radioactive decay. If you can arrange a sufficiently large key that is represented by a number of decaying radioisotopes and arrange that key with a error correcting code, then you would have a predictable loss of the key within a certain time window that's a function of losing N bits of data at a rate determined by the half-life of the radioactive media combined with the M bits of losable key.

This still leaves the idea that a partially decayed key provides a better place to start than a fully decayed key, but then we're back to math about the number of attempts to fix the errored key and that's a mathematical combination as well. Once the key is decayed such that half the bits are likely wrong after the error correctable size then your data would be guarded just as well as if an attacker had nothing.

Doing the time-related math for your selected radioactive material and EC code is an exercise for the reader.

If time is the constraint, then use time as the solution.

One Time Passwords can use time-synchronization as a factor. You could design a system whereby a OTP algorithm is required, but use the time-sync portion not only to verify the OTP, but also as a check to see if the time threshold has been exceeded.

If I understood what you want correctly, in special the hard drive example, then no.

Because if someone was able to read the message during some time, it means that he was able to save it form the computer to a flash disk, print it, extract it from the computer memory, copy it using pen-and-paper, photograph, audio/video record it, memorize it, speak it aloud etc. So even if the media is degraded, the message was saved again in some other media, even if the media is the brain of the person who read / listened to the message.

But if your scenario doesn't include that, and you mean that the message was stored in some computer that was totally secured, and that you want to be able to retrieve the information just during some specific time, and not before/after that, then yes: you can encrypt it using the strongest encryption you have, and then have some third party provide you the key just at the specific time. Since no-one would have access to the computer, the key would be able to decrypt the message only during that time. Before, brute-force would fail. After, the key wouldn't be provided. And instead the problem being your computer, it would go to the 3rd party providing the key.