The problem isn't that these algorithms might have their keys/inputs brute-forced. Given large enough keys and/or input sizes, they almost assuredly won't.
The problem is that there exists no crystal ball with which to assert whether or not a particular algorithm will still be considered strong through the next two hundred years of cryptanalysis. We currently believe these algorithms are strong, but these beliefs are either based upon empirical evidence (e.g., the AES algorithm itself hasn't been broken by the world's foremost cryptographers) or mathematical assumptions (e.g., RSA is "hard" to break assuming factoring is "hard", and ECDSA is "hard" to break assuming the DLP is "hard").
Additionally, we have no generic way of asserting that complex use-cases of secure cryptographic primitives is strong. GPG is built upon RSA, AES, and SHA. Even if we take as an axiom that each of those primitives are strong, the specific composition used by GPG may be found to be weak. For something more real-world, TLS has gone through many revisions, each thought at the time to be relatively secure, and each time discovered later to be subtly (or egregiously) broken.
Even if we somehow demonstrated that the primitives and compositions are secure, we still run into problems. These algorithms are written in software, and software is written by humans. Humans are imperfect, and we make mistakes. The Debian distribution of GNU/Linux, for instance, made seemingly-innocuous changes to OpenSSL that resulted in its random number generator being extremely predictable. In many cryptographic use-cases, if your random number generator is broken, the entire system is broken. Heartbleed is recent example of something that wasn't necessarily insecure being implemented in an insecure fashion — leading to catastrophic compromise of sensitive data on servers worldwide.
Finally, even if we have a bug-free, formally verified implementation of mathematically-proven cryptographic protocols, the other software on the computer could be insecure or improperly-configured and vulnerable to compromise. Your Bitcoin wallet may be strongly-encrypted, but this doesn't matter if your Windows machine gets a virus that snoops on your keystrokes. People themselves are also a weak link; research has repeatedly demonstrated that people will pretty much hand over whatever sensitive information is asked of them for a piece of candy or an animated GIF of a cat.
TL;DR, will your data today be safe in two hundred years? I wouldn't bet on it.