There seems to be three different notions mixed up here. Suppose your system has a secret key, and that your question should be understood as asking how the quality of that key changes over time, and how that relates to the concept of Entropy. In such case:
- How much entropy does a key have to have, for your system to get adequate security strength?
- How much entropy did the key get by the way it was generated?
- How much Shannon-entropy does the key retain by being kept secret in the long term?
Regarding the first notion, it should be stressed that the entropy of a key doesn't change, just because the limit of what counts as adequate security strength changes over time.
In cryptography, Entropy usually refers to the second notion only. One way to look at it is to note that cryptography is about systems where the entire security of your system, ultimately depends on the secrecy of the secret key. If your system does a poor job at keeping the key secret, it might be a problem with your cryptographic schemes being susceptible to cryptanalysis, or a problem with your key management. If the key doesn't stay secret because it was poorly generated, it is a problem with the amount of entropy it got from the way it was generated. Those are two different questions that have to be handled differently in cryptography, so it makes sense to define Entropy in such way that only refers to the latter.
Regarding the third question, it might however be noted that Shannon-entropy is a measure of the unpredictability of the key in a more general sense. Interpreted in absolute terms, this means that a key can only have entropy until it is generated. Once it is generated and has been used once, it gets a specific value, can only have that one value and consequently has no entropy. (This, btw, is why you can only get information theoretic security from an OTP and why it mustn't be reused.) In relative terms, the key might still be unpredictable to a specific observer (and in that sense still have entropy relative to that observer), and this kind of entropy might of course degrade over time, as the observer learns information about the key (e.g. due to cryptanalysis or because of poor key management).