The fan switch is probably bad. My Ford Explorer did that, I had to have the switch replaced.
This could also be caused by a bad blower motor resistor.
Defective Heater Resistor Pack.
The 2004 Chevrolet trailblazer air conditioning fan switch has three settings. The switch can malfunction, and only work in the high setting.
Had one that the fan motor was going bad Was burning out resistors with high draw
blower motor resistor
the blower motor resistor is bad or the connector going to it
The fan control module in the engine compartment has gone bad.
If only high speed is effected check the high speed relay and/or the fan switch/electrical connections for problems.
the blower motor resistor is bad or the connector going to it
Blower motor resistor...around $25 on eBay
Bad resistor or a malfunction in the switch.
try replacing the blower motor resistor
You need to replace your Blower relay,