Unless the shaft is snapped off, volume controls usually don't "Fail", but they can get really dirty causing the volume level to be scratchy, with one side, the other side, or both to drop out when turning.
The SX-1050 uses a sealed volume control, so its not easy for someone without experience to clean it.
To get to the control, the cover has to be removed, the front panel and knobs have to be removed, and the board with the volume control needs to be pivoted out of the chassis, to get to the 2 screws that hold the control together. Those screws, and small nuts behind have to be removed, and the sections need to be carefully pivoted open just enough to spray some cleaner, and then some faderlube into the openings. I believe there are 2 sections to that control, but could be 4. Advising again that if you don't have experience with things like this, find someone who does.