Yes, running a car on low fuel too often can cause several problems or damage to the vehicle. Here are the key points explaining why:

Fuel Pump Damage:
The fuel pump relies on gasoline for lubrication and cooling. Running on low fuel means the pump is not submerged fully, leading to overheating and wear, which may result in expensive repairs.

Sediment Build-up:
Over time, debris and sediment accumulate at the bottom of the fuel tank. Running the car on low fuel increases the chance of this sediment being drawn into the fuel system, potentially clogging fuel injectors and filters.

Fuel Pump Strain:
A nearly empty tank forces the fuel pump to work harder to draw in fuel. This constant strain can lead to premature pump failure.

Engine Misfires:
Low fuel levels can cause inconsistent fuel delivery, leading to engine misfires or poor performance, which may damage the engine over time.

Risk of Stalling:
Running out of fuel increases the risk of the car stalling unexpectedly, which could lead to dangerous situations, especially on highways or in high-traffic areas.

Reduced Fuel Efficiency:
When the fuel pump struggles to pick up fuel, the engine may not run efficiently, leading to lower fuel economy and increased consumption.

Air Intake Issues:
Running on low fuel can introduce air into the fuel system, leading to poor engine performance or difficulty starting the car.

Catalytic Converter Damage:
Consistently running out of fuel can harm the catalytic converter, as a misfiring engine can send unburned fuel into the exhaust, damaging this expensive component.

It's best to keep the fuel tank at least a quarter full to avoid these issues.