Quick reaction: Start a rumor that C-suite is looking to axe the deadwood in their middle management, and sees "managers not aligned with the company's priorities" as obvious targets.
The fix for this situation, more-or-less, is learn what you can about the customer's internal issues, then have an experienced and diplomatic manager of your own play a few rounds of golf with the customer's C-suite. There may be some good reasons for the resistance you're facing. Or "understandable" reasons.
(Not saying that diplomacy is easy, nor that favorable results are assured.)