Feeling like an emotional punching-bag and not sure what to do

So this is pretty complex. I have Borderline Personality Disorder, and which I found out about almost a year ago now. I've been with my boyfriend for maybe 10 months of that, so he's really been around since I started learning all about this illness and made some major changes in my life. My previous relationship died during a long dissociative episode, but had been characterised for several months by what I feel now is emotional abuse of my partner - as I didn't know I was ill, I blamed him for everything I was feeling and treated him in a way I am now deeply ashamed of. He would often ask "Why aren't you this way with other people? Why is it just me?" And I wouldn't have an answer, of course. I didn't know I was wrong.

Fast forward to now. My current partner was in the midst of an episode of depression when we met, but with some nudging he sought therapy and has emerged from that fairly happy and healthy. He has trouble with anxiety and feelings of worthlessness, but the full-blown depression has not returned.

For perhaps the last six months, these feelings seem to have been worsening despite undergoing CBT. He's been given a chart listing "distorted automatic thoughts", and although he's been able to reclaim his motivation and zest for life, he's been unable to shift these destructive thinking patterns. A seemingly innocuous comment from me will often (through a distorted interpretation) lead to disproportionate anger and resentment, hyperbole, defensive behaviours, all kinds of hurtful statements, swearing, refusing to talk to me, and often the imminent threat of break up.

This is complicated so much by my BPD: knowing what I have but not always when I'm doing the wrong thing leaves me dizzy and confused, unsure if it's his problem or mine at times. Often the idea of breaking up comes from me unable to emotionally deal with how much he seems to resent me (as though I'm a burden he can't get rid of), and he will simply not disagree that one of us should leave.

Why are we still together? It's the most rewarding relationship I've ever been in. He can feel emotions on the same level as I can, so when we share happiness and excitement and love, I feel connected in a way I can't to most people. I'm aware that it's this high that brings the danger of the collision of our intense lows, but I'm willing to work through them.

The question is, what should I do? He's stopped therapy: He ran out of sessions covered by medicare, I'm on a pension and we can't afford to pay for more on an ongoing basis (though if I knew it would help, we would make it work). However, we can't seem to get past this roadblock of his inability to recognise the thoughts he's having as distorted. I can count the number of times he was honestly able to catch himself and say "no, that's distorted" on one hand - the rest of the time, things get various levels of nasty before we can break through and help him see how he's skewed events in his head and reacted disproportionately. I honestly see so much of myself last year in him. I wonder why it is that I was diagnosed with something with a name, when he's going through almost EXACTLY the same things, which are to me, very different from anxiety and depression. I don't want to lump him into a box, but could there be something else going on here? Is there a reason the CBT might not be taking, and what can I do?