When a key customer keeps claiming low service quality although your company trying to keep highest quality, what would you do ?

I would recommend to go for a service level agreement with the customer with mutually agreed service parameters. This will give no scope for disputes as both will have to agree upon the service levels achieved at the end.

Examples of measurable service parameters:

Agreed response time from the time of complain logged.

Agreed average monthly uptime of the equipment supplied.

-First show empathy and be grateful that your  key customer is providing you with such valuable insight. (Many would just leave without the opportunity for you to improve).

-Now ask questions that allow you to understand in detail what exactly is not working (ask for examples).

-Once you clearly understand the issue, suggest a possible scenario of improvement and ask for feedback.

-Agree and implement (If SLA exist, adjust accordingly)!

-Follow up regularly!