CS stops defending, very frustrating

Casimir attacked a neighbouring city state early game so I sent a few units to check it out and hopefully disrupt his attack. There were a couple of polish spearmen left and I tried to block them off. I blocked one off into the water and the CS picked it off. At this point the CS is already at 0hp, with a garissoned CB. I blocked the other spearmen for a few turns hoping the CS will kill the surrounding archers but the CS refuse to shoot and let the polish archers free shot at it. At this point I gave up, and let the spearmen go. The spearmen spilled into the water again, and the CS killed it while embarked. Why did the CS only shoot at the embarked spear? Was it because its melee, or was it because its the only thing that can be killed in one turn?

The AI most of the time is useless at military strategy. It could be that it didn't see any immediate threat, and a city at 0 hit points does no(or very little) damage when it does its ranged attack. It could be that the AI considers a damaged city like a damaged unit, it needs to heal before it can attack effectively again(although a city heals regardless if it attacked or not).

Cities always deal full ranged damage