A fixed-pie concept of mediation has been largely criticized as being too archaic and too ego-centric to actually provide a resolution which satisfies all involved (Steinel et al., 2000). Instead, more simplistic and more conducive tools can be used to improve mediation and to overcome the impasse. For instance, simply striking a deadline so that all involved have to abide by it can provide the two parties in this case with a greater level of incentive in overcoming the impasse. For the two parties involved in this highly emotional situation, establishing a more useful precedent can also be effective: in this case the precedent might involve the ethical behavior in research in general, and might seek to inspire all involved to negotiate for more livable terms.

Finally, in such a case the mediator can just push for improved communication for all around: this can be done by setting ground rules and by leading via example. There should...

But the reality is that in this case, such an impasse should never have occurred. If a mediator was really doing his job correctly, he would have anticipated a potential impasse and would have been successful at avoiding it in a more adept and focused manner. In truth, the impasse should never have happened, as most likely occurred from a lack of experience or a lack of preparation on behalf of the mediator and through a lack of adequate education or probing questions.
References

Berman, L. (2014). Impasse is a Fallacy . Retrieved from americaninstituteofmediation.com: http://www.americaninstituteofmediation.com/pg70.cfm

Johnsen, J. (2013). The Dreaded Impasse. Retrieved from jsjmediations.com: http://jsjmediations.com/pdf/Impasse%20Article.pdf

Steinel, W (2000). Unfixing the Fixed Pie. Journal of Personality and Social Psychology. p.975-