Thanks for the chance to help. I am an attorney with over 12 years military law
The commander always has discretion. Always...that is why they are entrusted with the position of command. Every service has a rigorous command screening program to ensure individuals selected for command have the skills and competence needed for this important position.
So the commander has the final say.
There is no law or regulation that requires them to take action on complaints by service members.
That said, there are checks and balances in the system. For example, there is Art 138, UCMJ that allows a service members to file a formal complaint against their commander.
And there is the IG who can take complaints of unfair treatment.
So if a particular service member feels their commander is not being fair, they have avenues to pursue.
But to answer the question, there is no law that requires a commander to take action on a complaint.