A difficult message, done well.
STEP ONE: ESTABLISH THE FACTS
What actually happened. Not what the customer thinks happened, and not your assumption.
STEP TWO: DECIDE THE OUTCOME
What are you going to do? Decide before drafting.
STEP THREE: ASK FOR A DRAFT
"A customer complained about [issue]. The facts are [what happened]. I am going to [what you will do]. Write a reply that acknowledges the specific problem, takes responsibility, and states what happens next. No excessive apology."
STEP FOUR: CHECK IT ADDRESSES THEIR ACTUAL COMPLAINT
Not a general one. This is the most common failure.
STEP FIVE: CHECK EVERY COMMITMENT
Timing, refunds, replacements. Only what you decided in step two.
STEP SIX: ADJUST THE TONE
Toward how you actually speak to customers.
STEP SEVEN: READ IT AGAIN LATER
When you are not annoyed.
FOR PUBLIC COMPLAINTS
Every future reader sees your reply. Specific and measured reassures more than the complaint discourages.