What is Honda VTM4 Light and why does it stay on?

The Honda VTM4 (Variable Torque Management 4 Wheel Drive System)
There can be differences between Honda years, so be sure to read the manual for your specific Honda.

When there is an engine problem, the computer (ECM) shuts down VTM4 system.

It works automatically by adjusting how much torque is applied to the rear wheels depending on how much traction they are getting.

When there is normal driving conditions, only front wheel drive is used.
When the vehicle detects that the rear wheels are losing traction, the VTM4 system will send more torque to whichever wheel needs it, whether it be one or both.

The VTM4 lock button locks the rear differential to force the vehicle to send power to the rear wheels.

The VTM4 lock will disengage when the vehicle reaches roughly 18mph.

It is not suggested to turn the VTM4 lock on dry, flat roads, and/or above 15mph, as doing this could damage the vehicle.

What To Do if VTM4 Light Stays On?
Scan for other codes which will point to the problem.
For example, if a C003A Code Right Rear Wheel Speed Sensor is given, there likely is bad speed sensor.