is it possible for the cryptographic function to break?
short answer: yes
long answer: just fyi "breaking" could mean a few different things in this context. i assume you mean that an attacker has fully mapped SHA-2 so that he can determine your private key and spend your bitcoins.
anyone that could "break" SHA-256 right now could win a nobel prize and would likely launch a new branch of cryptography. it is just not feasible with our current knowledge of mathematics, quantum computing, and cryptography. in 5 to 20 years it could be possible, but if an attacker developed such technology, it would likely to be much more profitable to use it to mine than to search for the private keys of publicly known wallets.
with respect to bitcoins: satoshi anticipated the "breaking" of SHA-2 and outlined how bitcoin would adapt to a new cryptographic function before SHA-2 could be feasibly broken. the core bitcoin protocol doesn't really care which cryptographic algorithms is utilized, and the algorithm can be changed without disrupting bitcoin's functionality.
