US-led coalition airstrikes in Iraq have allowed the Iraqi Army, Kurdish peshmerga fighters, and their allies to reclaim territory lost to an Islamic State (IS) spring and summer offensive.

But in the Syrian city of Kobane, where Syrian Kurds and their allies have been fighting IS forces with dogged determination since September with the support of airstrikes, the gains have been especially slow. Despite losing fighters by the hundreds, the IS has proved difficult to stamp out, maintaining a solid foothold in the frontier town.

IS has also kept a grip on 381 villages in the wider district, villages the jihadi group seized with alarming speed in September, sparking an exodus of 200,000 people to Turkey. That offensive pushed the coalition to reconsider its strategy against IS in Syria and drew in reinforcements from Iraqi Kurdistan.

Kobane’s field commanders estimate that at least a third of the city remains contested or under the control of militants, figures that illustrate the challenges of close quarter combat.

“There are clashes in the east and the south,” says Kobane district chief Anwar Muslim. “IS forces are attacking us especially hard from the eastern front, but most of Kobane is under the control of the People’s Protection Units (YPG). We are coordinating with the Americans and informing them on IS positions.

“There is street fighting so it is very difficult to take new areas of the city,” says Mr. Muslim.

Airstrikes come quickly

In Kobane, the frontlines remain fluid – with clashes concentrating around Souk Al-Hal in the east and Mount Mish Tanour to the south. IS holds the high ground and a strategic radio tower in the west. “Sometimes our positions are so close that we can hear each other,” says Mohammed Abu Hassan, a fighter recovering from a gunshot wound.

“They yell: we are coming to kill you, infidels! They’ve brainwashed them and convinced them we are not Muslims. If their men are wounded or killed, they don’t fall back. If things get really bad, they are prepared to blow themselves up. IS fighters are convinced they will go to paradise and be rewarded with virgins,” he adds.

While the airstrikes have not succeeded in evicting IS from Kobane, they did stop the IS offensive in its tracks when it was threatening to overrun the city. They also imposed heavy losses in the militants’ ranks. Retired Gen. John Allen, the coalition’s coordinator, declared on Nov. 20 that IS had “impaled itself” on Kobane, losing more than 600 fighters. In December, the Syrian Observatory for Human Rights, put IS fatalities at 905.

Many fighters marvel at the speed and accuracy of the strikes, claiming that calls for help – channeled through a military operations room in Kobane – are answered within 15 minutes if there is a plane already in the air and no more than 45 minutes if one needs to be deployed.

Claims of Americans on the ground

Some say that there are two American officials deployed in Kobane to help coordinate the ground-air effort, a claim that could not be independently verified. The IS fighters have taken such a trashing that they use the lulls between airstrikes to evacuate their wounded. “They don’t even show their noses when the drones are overhead,” said a fighter on a break in Suruc.

Besides boosting morale, air cover has allowed Kurdish forces to stage attacks in areas outside their control. Guerrillas are striking IS in villages 25 miles from Kobane, according to Muslim. Meanwhile, Iraq’s peshmerga – now on their second rotation with 137 men – have helped bolster defenses within the city.

“Every day we fight, but there has been a lot of progress since we arrived,” says Maj. Izzedin Temo, an officer in the peshmerga forces who came to Kobane with a three-month mandate at the end of October. “God willing we will have two celebrations soon – New Year and victory in Kobane.”

The YPG, and its sister force of female combatants, the YPJ, are the main striking force in Kobane, bringing together thousands of men and women trained in guerrilla warfare. Their leadership coordinates the movements of the peshmerga, the only fighters with heavy weapons, and allied forces of the Free Syrian Army.

Those who have fought IS before, worry the battle in Kobane will drag out.

Supply lines broken

“Before the air strikes, IS held similar positions to now but in greater force,” says Faris al-Qayyem of the Raqqa Revolutionaries Brigade, which fights alongside the Kurds in Kobane. “If we killed 100 fighters in one day they were immediately replaced, just like ants. Now their supply lines are broken, their convoys destroyed.”

“The battle of Kobane will take a long time, but we will be victorious,” he predicts.

Commanders say the strategic priority is to control Kobane and to protect the civilians who stayed behind. Roughly 80 families decided to brave winter in a war zone rather than seek shelter in neighboring Turkey. In the Turkish town of Suruc, just a short walk across the border, Kurdish volunteers work round the clock to send food and medicine boxes.

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“When it comes to medical supplies, we have nothing,” said a volunteer in the city.

A suicide attack at the end of November destroyed the last standing hospital in Kobane. The explosion rocked the border crossing linking the town to Turkey. Kurdish officials and Syrian Arabs who took part in the subsequent clashes say IS forces crossed into Turkey to stage that attack, an assertion that Ankara vehemently denied.