What is stopping someone from saving encrypted info, and decoding it later? When I send encrypted data to a website, using public key encryption, what is stopping someone who is listening from storing my encrypted data, and decryption it in a few years after they have determined the private key?

From my understanding, private keys can be discovered after a few years using a fast computer.
Are there any time-sensitive safeguards used with public key encryption so that my info won't be useful in a few years?
Decoding information within a time frame is of absolute importance.

Say X is an terrorist, the information of his attack will be useful today, not years after the attack has happened. And similarly decoding your message is important today, not years later. Also there might be a possibility that when somebody has decoded your key for future use, you might have already changed it.