US air strikes are failing to drive back Isis in Iraq where its forces are still within an hour’s drive of Baghdad.

Three and a half months since the Iraqi army was spectacularly routed in northern Iraq by a far inferior force of Isis fighters, it is still seeing bases overrun because it fails to supply them with ammunition, food and water. The selection of a new Prime Minister, Haider al-Abadi, to replace Nouri al-Maliki last month was supposed to introduce a more conciliatory government that would appeal to Iraq’s Sunni minority from which Isis draws its support.

Mr Abadi promised to end the random bombardment of Sunni civilians, but Fallujah has been shelled for six out of seven days, with 28 killed and 117 injured. Despite the military crisis, the government has still not been able to gets its choice for the two top security jobs, theDefence Minister and Interior Minister, through parliament.

The fighting around Baghdad is particularly bitter because it is often in mixed Sunni-Shia areas where both sides fear massacre. Isis has been making inroads in the Sunni villages and towns such as in north Hilla province where repeated government sweeps have failed to re-establish its authority.

Mr Abadi is dismissing senior officers appointed by Mr Maliki, but this has yet to make a noticeable difference in the effectiveness of the armed forces, which are notoriously corrupt. During the battle for Mosul, Iraq’s second-largest city, in June, Iraqi government forces nominally numbered 60,000 in the army, federal police and local police, but only one third were actually on duty. A common source of additional income for officers is for soldiers to kickback half their salaries to their officers in return for staying at home or doing another job.

The same system is universal in civilian ministries, which have far more people on their payroll than are actually employed.

A World Bank report just published reveals that out of 8,206 guards employed by one ministry only 603 were actually working. Some 132 senior officers have recently been sacked by Mr Abadi, but there is as yet no sign of the army being able to make a successful counter-attack against Isis. Worse, in Baghdad it has been unable to stop a wave of car bombs and suicide bombers, which continue to cause a heavy loss of civilian life.

An example of the continued inability of the Iraqi army to remedy the failings, which led to its loss of Mosul and Tikrit, came on 21 September when Isis overran a base at Saqlawiya, near Fallujah, west of Baghdad after besieging it for a week.

The final assault was preceded, as is customary with Isis attacks, by multiple suicide bombing attacks. A bomber driving a captured American Humvee packed with explosives was able to penetrate the base before blowing himself up.

This was followed up by an Isis assault team dressed in Iraqi army uniforms. Some 820 government soldiers stationed at the base broke up into small groups and fled by backroads but were ambushed.

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What is striking about the loss of Saqlawiya is that during a siege lasting a week the Iraqi army was unable to help a garrison only 40 miles west of Baghdad. Complaints from the troops that they were left without reinforcements, ammunition, food or water are very much the same as those made in the first half of 2014 when rebels led by Isis outfought some five government divisions, a third of the 350,000-strong army, and inflicted 5,000 casualties.

Fallujah fell in January and the army was unable to recapture it.

The US could embed observers with Iraqi troops to call in air strikes in close support, but people in the Sunni provinces are frightened of being reoccupied by the Iraqi army and Shia militias bent on revenge for their defeats earlier in the year. In areas where there are mixed Sunni-Kurdish populations both sides fear the military success of the other.

The military reputation of the Kurdish soldiers, the Peshmerga, has taken a battering since their defeat in Sinjar in August where its troops fled as fast as the Iraqi army had done earlier. The Peshmerga have not done much fighting since 1991, except with each other during the Kurdish civil wars, and even in the 1980s their speciality was rural guerrilla warfare, wearing the enemy down with pinprick attacks by 15 to 20 fighters.

Before the deployment of US air power, Isis in Iraq used motorised columns with 80 to 100 men which would launch surprise attacks.

With the possibility of US air strikes, this kind of highly mobile warfare is no longer feasible without taking heavy losses, But Isis has shown itself to be highly adaptable and is still able to operate effectively despite US intervention.

The problem for the US and its allies is that even if Iraqi divisions are reconstituted, there is no reason to think they will not break up again under Isis attack. The main military arm of the Baghdad government will remain Iranian-backed Shia militias, of which the Sunni population is terrified.