In the context of almost every proposed causality violation mechanism I've seen seriously discussed, it really is can't, not won't.
There are plenty of mechanisms in which can't applies. There are others which don't have that limitation. I don't even want to touch what qualifies as 'seriously discussed'. I'm really not up to date with which kinds of time travel are high status.
Ignore status issues. Instead focus on time travel mechanisms that don't violate SR. Are there any such mechanisms which allow such violation before the time travel device has been constructed? I'm not aware of any.
http://www.nature.com/news/2011/110922/full/news.2011.554.html
http://arxiv.org/abs/1109.4897v1
http://usersguidetotheuniverse.com/?p=2169
http://news.ycombinator.com/item?id=3027056
Perhaps the end of the era of the light cone and beginning of the era of the neutrino cone? I'd be curious to see your probability estimates for whether this theory pans out. Or other crackpot hypotheses to explain the results.