What predicts the severity of rejection pain? A number of studies show that social rejection causes actual pain. Is there a study that focuses on finding the personality dimensions that predict the amount of such pain? For example, is there a correlation between extroversion and the severity of rejection pain?

An answer nearby suggests that there is some kind of "sensitivity" to a person, but I am so far unable to determine what exactly this "sensitivity" means.


References:
K. D. Williams and allies — "Ostracism: Consequences and Coping"
Naomi I. Eisenberger and allies — "Does Rejection Hurt? An fMRI Study of Social Exclusion"
I have found 2 papers that may be relevant to your question - 

This paper probably answers your question the most - I have only schemed  through it, and it seems that the results were insignificant.  You can check out the paper in more detail, hopefully it will get you to more resources that can help with your research.

I have also found this paper which does not entirely answer your question, but I think will help with your insight.

Also keep in mind that some neuroimaging research on social exclusion in causing activation in regions (e.g. dACC) associated with physical pain employs reverse inference method.  This does not mean the results are entirely unworthy of considering - just something to keep in mind when looking at neuroimaging result interpretations.

References

McDonald, Melissa &amp; Donnellan, M.. (2012). Is ostracism a strong situation? The influence of personality in reactions to rejection. Journal of Research in Personality. 46. 614–618. doi: 10.1016/j.jrp.2012.05.008.

Park, M., Lee, K.H., Sohn, S., Eom, J., &amp; Sohn, J. (2014). Degree of extraversion and physiological responses to physical pain and sadness. Scandinavian journal of psychology, 55(5), 483-8. doi: 10.1111/sjop.12144

Poldrack R. A. (2011). Inferring mental states from neuroimaging data: from reverse inference to large-scale decoding. Neuron, 72(5), 692–697. doi: 10.1016/j.neuron.2011.11.001