I don't think we'll learn more about this short breakup until the trial. If it is to their advantage, the prosecution will ask CS about this when he is on the stand. So far no one has corroborated the short breakup as far as I have seen in the media.
CS said that KA dated others during the breakup, so I am surprised no one has come forward to tell their story to the media. It may be because they don't want to be associated with this case, to be seen as connected to KA in any way. They may hold positions in the Austin community that wouldn't be good for them to come forward, and it could be that their employers don't want the notoriety. They they may have to testify at the trial, however, if they are subpoenaed.
And perhaps someone that KA dated during this short breakup had a significant other, and so would prefer not to come forward.