Without knowing anything about your product, I have to disagree -- especially for "turn-key" solutions.
The turn-key solutions that I've had the pleasure (sic) of delivering depend in no small part on post-implementation support (disclaimer: I manage telecom infrastructure deployments). This seems to be the case (and yes, I'm generalizing here) for complex software solutions that have either many components, or are sold as a single complex point product.
Quick, effective customer support in the form of P1 issue resolution would be the second highest praise one aims to receive from a customer. Your point about the "best customer support is customer support that is not needed" is the highest praise of all (especially in an infrastructure play).
Quality customer support undoubtedly helps with customer satisfaction and often is one of the underlying factors to sales' ability to up(sell|grade) existing customers.
Your unhappy customers may be a marketing or sales issue; not necessarily a customer support problem.
As such, without additional information, my answer is "F", qualified with "you may have framed this question incorrectly."
Customer support can be considered a last line of defense to help resolve deeper issues, such as fundamental dissatisfaction with the product. The feedback that you hopefully take back from disgruntled customers should be fed back to your sales and marketing organizations to understand if the problems are indicative of a larger trend (i.e. product/solution not meeting needs of key customers), or if the lost customers were one-offs with specific circumstances unlikely to 'spread' to other customers.
EDIT: Added last paragraph.