Some legal experts on CNN disagree, they say Bannon can take it to court and file appeals if he loses, effectively tying it up for an indefinite period.
The only way this can happen is previous SCOTUS rulings are ignored, and the courts all of a sudden believe citizen's have executive privilege's. Bannon's reasoning for ignoring the Subpoena is because Trump, a citizen who hold's no office, told him too. Trump has no more authority than you or me, telling Bannon to ignore the Subpoena, and Trump has no more executive privilege's than any other citizen, as he is no longer in office. SCOTUS has already recognized Congress's power to issue Subpoena's, and that power is broad, all though not unlimited, as it cannot be used for political gain or to investigate someone to find out if that person (the person they subpoenaed) committed any wrong doing. A Congressional subpoena must potentially further some “legitimate legislative purpose,” per the SCOTUS. This subpoena is 100% for legitimate legislative purposes, the investigation into 1/6. If Bannon tries to take it to court, It will make it as far as Trump's 60+ voter fraud cases that where thrown out, and will be ruled on just as quickly. Bannon could also sit in jail, as Jhhnn stated, during this process.