Cases are not necessarily dropped after an alleged victim changes their testimony. An altered testimony does not prevent charges from being filed. What takes prevalence in those cases is the evidence found at the time of the arrest, the evidence found when the incident occurred, and the evidence found when it was reported.
Unfortunately, victims of domestic violence can have what is called Battered Spouse Syndrome, where someone in an abusive relationship cannot fully comprehend the abuse they’re under, and it’s unreliable. It commonly occurs when victims change their testimony due to the trauma they’ve suffered or out of fear, so it’s not a complete guarantee that the charges will be dropped for those reasons.
Issues may arise if the case goes to trial and the victim recants everything; however, if there is sufficient evidence that the incident occurred, it might be unnecessary for the victim to testify.