The problem described in this question is not isolated to people with borderline personality disorder (BPD). It is quite common for people with mental health problems to be resistant to the idea of seeking out treatment.
There are so many reasons that people refuse to get help. Many are afraid of the stigma attached to mental health issues. Others feel they cannot commit the time and/or financial resources required to engage in therapy. Some may not be willing to admit that they have a problem in the first place, or may not think that treatment will work for them (despite clear research evidence to the contrary; we now have a number of effective treatments for BPD and a host of other mental health conditions).
Whatever the reasons may be, being the loved one of someone who is engaging in self- (and sometimes other-) destructive behavior, and refuses to take steps toward change, can be heart-wrenching. In this position, many loved ones feel the need to do something that will convince their loved one to get help.
Unfortunately, if your loved one is an adult, you have no control over what they do or don't do. This lack of control leaves many loved ones feeling desperate and helpless, but this is the reality. Dr. Marsha Linehan (the psychologist who developed Dialectical Behavior Therapy for BPD), said it best in a recent piece in the New York Times; she wrote: "If another person does not see the need for getting help, it is their right to not do it. Sorry."
This doesn't mean there is nothing that you can do. There are support groups and resources for loved ones of people with BPD. Getting involved in these groups and educating yourself about the disorder can help you better understand BPD and make choices about how you want to live your life in relation to your BPD loved one. Your energy is probably better spent on these activities, which are in your control, than on changing your loved one's behavior, which is not in your control.