Going into a negotiation, there is an assumption that you will come to an agreement. If you are unable to agree terms this is often viewed as a failure but whether or not it is depends on how well you have prepared.
Before you start a negotiation it is important to think through potential outcomes. Which party has most to lose if you cannot agree? If you have done your homework on Standards you will know the range of acceptable outcomes. If you cannot get to a deal in this range, which side is most adversely impacted?
You should be able to answer this question for both sides and for individuals on both sides. e.g. perversely a product manager incentivised on average margin may be more inclined to lose a large customer than give them a significant price cut to stay. However there is a cost to switching suppliers as well as acquiring and on-boarding customers, and moving away may be the wrong decision for both organisations. One option is to adjourn the conversation with the product line and find someone with a more holistic view. Even then they may overestimate the value of inertia, so you have to make them believe there is a real possibility of losing your business. Properly research the alternatives and be prepared to walk away from a deal if your minimum requirements cannot be met.
Also remember that walking away or 'taking the deal off the table' is not usually the end of the process and may be the only way to break an impasse. Deployed as a tactic however it should be a last resort. Used frequently/disingenuously it loses effectiveness very quickly and can create resentment and distrust.