Diagnosis
The button or membrane switch on the control panel is likely faulty, or the signal isn't reaching the main circuit board. Less commonly, the fan motor's speed control circuitry has failed.
How to Fix It
Try using the remote to change fan speeds. If the remote works, the issue is localized to the physical button on the heater unit. You can try pressing the button firmly multiple times to see if it's a contact issue.
If That Didn't Work
If neither the button nor the remote can change the speed, the control board's triac (the component that modulates power to the fan motor) is probably dead. This isn't repairable at home.
Heads Up
Running only on high speed can dry out the air and be noisier. Running only on low speed might not move enough air across the heating element, potentially leading to overheating over time.