Why was the battle of Basra called off?

Among many possible reasons:

1) The Iraqi army got its ass kicked. This would be a sound reason to stop and re-group. I find this unlikely. In most battles that pit conventional armies against irregular troops, the conventional army will win a stand up fight just about every time. Exceptions do happen. If so, this does not mean that Iraq has lost the war. Winning a war does not mean that you did not lose any battles.

2) The Iraq army achieved its objectives. Possibly, except we will probably not know what the ‘real’ objectives were for quite some time. From the accounts that I am reading, this also seems unlikely.

Please note that these two ideas are from the Iraqi army's perspective. The same reasons can apply for the other side. Also note that the two ideas are at the extremes. In other words, most of the other reasons will fall somewhere in between the two ideas I have presented.

The battle looks more like a draw. The ‘Fog of war’ prevents us from seeing events all that well. Beware of conclusions about who won the battle. It will probably be some time before we really know who made out best. Even then that can be problematic. Witness how reporting still is insisting that Israel lost the battle against Hezbollah in August of 2006. Losses have been well documented and confirmed. Hezbollah lost a significant percentage of its combat ability. The Israeli Defense Force (IDF) did not. This may not win the war, but it tells me that Israel won the battle.

The Iraqi army was the driving force behind the assault on Basra. The resistance the Iraqi army encountered apparently surprised them. Maybe they need to use a different approach. I don’t know what tactics they employed, but I have heard that maybe they should use a similar idea that the U.S. implemented for the ‘surge’ in the Basra region. Maybe this is what they were attempting, but the resistance was far greater than they expected. Once again, the "Fog of War" is preventing us from seeing much.

The Iraqi army used units to spearhead the attack that had not seen any combat. This is a rookie mistake that I would expect not to be repeated. The ‘new’ units behaved as most unblooded units have throughout history: They were indecisive, took too long to mop up light resistance, panicked in situations that were not as bad as they may have appeared. The loyalties to each other and the teamwork that is needed in combat were tested early before they could be well established. These are common problems in all ‘new’ combat units. In addition, Iraq has problems with loyalty. The culture of the Middle East is loyalty to your clan over everything.
This is one of the issues the war is about. Desertion rates can be expected to be higher than in other armies in other parts of the world. Particularly in units that have not been ‘bloodied’ yet.

In any case, Iraq is still a war zone. We can expect violence to rise and fall periodically from time to time. Just because the amount of combat is going up or down does not necessarily tell us who is winning. Don’t forget how wartime reporting sees everything through a political lens. Politics and warfare do not mix well. Politics can distort the view, sometimes beyond recognition. Wartime news reporting is particularly bad at the fundamentals of warfare. I suspect this is because news reporting is so good at politics that they tend to see warfare in political terms.