The auger (right side) lever can be held down by the drive clutch (left) lever. There's a shaft that connects the two of them, and a cam lock boss and spring that makes the mechanical connection.
If the auger lever isn't staying put, start by inspecting the linkage, and pay close attention to the cam lock boss. Make sure nothing is binding or stiff, and is properly lubricated with a light touch of general-purpose grease where indicated.
Be sure the return spring is in place, as well as the washers, cotter pin, and the small ratchet hardware is okay. Inspect the bushings near the cam lock boss for wear or slop, and be sure all hardware is properly tightened.