I'm so sorry this is happening to you. It makes no sense and is very unfair. I know how hard it is to fight for what you need when you are alone and afraid and exhausted just from daily life.
But looking at your messages, I wondered...
What have you to got to lose except your life?

BPD is a deadly illness. 1 in 10 people with BPD will die of completed suicide. Please, please, make a fuss. If you're getting nowhere with your psychiatrist, go back to your GP, being clear about what you are asking for. Use the NICE (National Institute of Clinical Excellence) Guidelines for BPD, which state that 'Mental health trusts should develop multidisciplinary specialist teams and/or services for people with personality disorders.' The guidelines also talk about providing twice weekly psychotherapy.
Borderline personality disorder (BPD)

(Interestingly, the guidelines also contain a whole section on 'Managing endings and transitions' which say that withdrawing services should be 'discussed carefully beforehand' with service users, who 'should be supported during the referral period' to other services and 'arrangements for support agreed beforehand'. Wave this document in the face of the organisation your departing therapist works for.)

Does your local Trust have a PD service? If not, what do they offer services users with PD? If it's not adequate or evidence-based, fight the trust to fund your treatment with a neighbouring Trust which does have adequate services. There are organizations which have mental health advocates who can help you to fight. If you are LGBT, and live in London (quite specific I know!), PACE have an advocacy service. Otherwise, these look like useful links:
Advocacy in mental health - Mind
Advocate for Mental Health
And this Independent Health Advocacy Service will help you complain about your current situation:
Independent Health Complaints Advocacy - SEAP

I understand the urge to lie down and die. I do. But if you possibly can, please kick up the fuss of your life. Your life is worth it.