I'm a defense-minded guy. Off the top of my head...
1 - Failure to secure adequate water supply, or protect it from poisoning.
2 - Failure to secure adequate food supply, or protect it from fire.
3 - Failure to provide adequate security to protect the life of the decisive leader of the resistance to the siege (civilian, military, and/or religious).
4 - Failure to prevent infiltration by spies. (Guards on walls, adequate passwords, adequate inspection of incoming and outgoing parties or individuals).
5 - Failure to prevent internal betrayal (mistreatment of senior military officials, relatives of the ruling families, intelligent minorities).
6 - Inadequate tactics or poor defensive posture. (Not anticipating attempts to undermine walls. No preplanning for defense against wall scaling, concentrated battering attacks, strategic movement or bunkers to avoid artillery).
7 - Simple geographic short-sightedness. (Leadership chose to hole up in just the wrong damn city when they could have held out forever someplace else).
8 - Poor character - Loyal forces could break the siege but the Leadership needing rescuing was led by A**holes, so their countrymen decided: Why f**king bother?
9 - Simple bad luck - You are under siege by the Empire of the Mongols or the United States (after 1900).
