There is an easy way to avoid the perception of failure in negotiations: don’t ever do anything risky.  Set the bar for success super-low, and you are likely to succeed every time at doing at meeting that (low) goal.  
Fear of failure dominates many negotiators, leading them to take few risks.  A basic reason is what Carol Dweck calls the “fixed mindset” – the belief that how you do is determined by who you are, that is, by your fixed characteristics.  These people are determined to show that they can do well, because they think that if you fail, that is because you are a failure. In this view, ability shows up on its own: if you have it, you have it, and if you don’t, you don’t.
In her book Mindset: The New Psychology of Success, Dweck contrasts the “fixed mindset” to the “growth mindset,” which is the belief that basic qualities are things that can be cultivated through effort, strategy, and help from others.  People with a “growth mindset” relish challenges as an opportunity to grow.  When they fail, they resolve to do better next time – they develop a plan for how to address the problems which held them back this time.
Negotiators do better if they can recognize when they are coming up against people with a “fixed mindset,” whether on the other side of the table or in their own organization.  An important signal is that the “fixed mindset” leads people to avoid unpleasant situations and unpleasant facts.  Dweck’s research has shown that people with a “fixed mindset” badly overestimate their abilities and how well they do in any given situation – after all, to them, any shortcoming is a sign that they just don’t have what it takes to succeed.  Of course, no one is perfect, but honestly facing the facts is just too threatening for people with a “fixed mindset.”
Another sign that someone has a “fixed mindset” is their approach towards effort.For them, making an effort is terrifying.  They think that successful people don’t need to make an effort: they do well because they are geniuses.  So there is no need to do a lot of preparation or practice for a negotiation: you either have it or you don’t. Trying and still failing is the worst fear imaginable for someone with a “fixed mindset.” 
It would be wonderful if there were a magic reset button so that everyone with a “fixed mindset” could suddenly have instead a “growth mindset.”  In the real world, however, there are many people with a “fixed mindset.”  Any negotiator is sure to run in to such people all the time.
The key to working with people who have a “fixed mindset” is to realize what they are looking for.  They will thrive when things are safely within their grasp – when they can be sure that they will succeed. The challenge then is to cast any proposition in such a way that they can be confident they will achieve success.