I am always annoyed too when the A.I. still has missiles when I've long spent mine, but it isn't because it has more of them. If you watch the A.I.'s behaviour during battle you will notice three things: 1) The A.I. spends a lot of time running its skirmishers back and forth without firing, even when they are being pelted with missiles; 2) it has a tendency to charge its units before they have spent all their ammo; and 3) when do fire it is not always with the entire unit.

All this adds up to a far slower rate of missile expenditure. It does not have more missiles; it just does longer with the ones it has.

However, I have no idea what causes the siege bug.