You've got increased wartime pay to soldiers, and pay to defense contractors. Energy costs and munitions. Construction and military engineering...
...and then what? It's a counter-insurgency, it's not like the military is unloading cruise missiles or nuking cities or getting aircraft shot down. What costs so much? Once the conventional warfare ended, the military construction/engineering/bases were built, and all the troops and gear were in place, wouldn't the costs be not-so-highly elevated over keeping a standing army and regular training? Just ammunition, increased wartime pay, and defense contractors no?
I guess it's kind of an ugly supply chain in hostile territory in the desert, but Saudi Arabia and Turkey are nominally allied, so it shouldn't be too hard to buy/ship food and ammunition through there. There's lots of cheap oil and refineries nearby. Where's all the money going?