BEIRUT—After a two-year siege, al Qaeda’s affiliate in Syria and other insurgents on Wednesday captured the one remaining Syrian army air base in Idlib, a development that activists said effectively expelled the last of President Bashar al-Assad’s military from the northwestern province.

It was the latest in a series of setbacks for Assad in Syria’s bitter civil war, now in its fifth year. Syria’s embattled president has acknowledged the losses, saying the army has had to relinquish some areas in the north to better defend...