Hubeny's 1998 paper got a lot of people interested in determining whether cosmic censorship can be violated by dropping too much charge onto a black hole. It suggested that you might be able to get a naked singularity from generic initial conditions rather than requiring infinitely fine-tuned initial conditions as in the 1997 example by Choptuik.
The only more recent information I've seen about this was a video of a talk by Eric Poisson in 2011. In that talk, Poisson generalized Hubeny's work to spinning black holes, and claimed that his group had made progress on technical issues involved in computing the self-force on a test charge. Hubeny and others in the field had recognized the self-force issue and had realized that it made it impossible to reach firm conclusions about cosmic censorship.
In 2011, Poisson seemed to be optimistic that he'd be able to prove fairly soon that Hubeny's scenario wouldn't actually go.
My question is, what is the current state of research on this topic?
Hubeny, "Overcharging a Black Hole and Cosmic Censorship," 1998, http://arxiv.org/abs/gr-qc/9808043
Related but different: What prevents the accumulation of charge in a black hole? That question asked for a general explanation of what the mechanism was that would prevent overcharging. Mine is asking for specific information on a recent research program.