BAGHDAD — Iraqi forces, backed by American airstrikes and advised by American officers, have been making strides in Anbar Province, slowly taking back territory from the Islamic State.

But in Falluja, a city in Sunni-dominated Anbar that has been in the hands of the Islamic State longer than any other in Iraq or Syria, civilians are starving as the Iraqi Army and militias lay siege to the city. And elsewhere in the province, Shiite militias supported by Iran are carrying out kidnappings and murders and restricting the movement of Sunni Arab civilians, according to American and Iraqi officials.

For seasoned observers of the American military involvement in Iraq — going back more than 25 years to the start of the Persian Gulf war — it is all part of a depressingly familiar pattern: battlefield gains that do not bring stability in their wake.

“Unfortunately, as has been a trademark of American involvement with Iraq at least since 2003 (and arguably since 1991), military success is not being matched with the commensurate political-economic efforts that will ultimately determine whether battlefield successes are translated into lasting achievements,” Kenneth M. Pollack, a senior fellow at the Brookings Institution and a longtime Iraq analyst, wrote recently in an online column.