Is my partner cheating on me... AGAIN?

My partner and I have been living together for 3 years. He has tried to cheat with at least two women that I know of, both in the first 6 months of us living together. He lied to me about it, but after seeing a couples therapist, eventually came clean saying he wanted to have sex with these women but "it didn't happen." He admits to visiting his most recent ex and walking into her bedroom naked with an erection, but she said no. The second time he arranged to meet another ex in a motel room, but he says she didn't show. Personally, I think he did cheat, but I have no actual evidence.
I also found out that he was talking to a woman online when I went to work. This woman was kind enough to send me a copy of their conversation when she discovered that he had a partner. The conversation was not sexual, but he complains about me a lot saying he is not happy and will leave "when the time is right". At the time, he had no job and I was supporting us and paying all the bills.
He also was (and possibly still is) talking to yet another ex on the phone. I objected and he said he would stop, but continued talking to her in secret. (I spied on his phone logs) He again said he would stop, but I heard him in his shed talking to a woman on the phone. His usual phone was in the house. I think, but he denies, that he has a second phone.
Eventually, I had a nevous breakdown and was admitted to a mental hospital for 3 weeks. While I was there, he moved all my gear into his shed and said I was not welcome back. As I could not find a house to rent at short notice, he allowed me to sleep in his shed.
He changed his mind after a few weeks and
after counselling and therapy we decided to try again with no lies, no abuse and mutual respect. We are both on medication and continue individual therapy. He has been diagnosed with Borderline Personality.
Fast forward 6 months and I am again suspicious. I had to quit work because of my depression and anxiety and he is still not working so we spend most of our time together. The other day however, I had to drive my adult son to hospital and was gone all day. That night, my partner was not interested in having sex. He said I could try, but he needed to "recharge his batteries because we had sex only.... " Then he stopped himself and said... "a couple of days ago."
We had last had sex 2 days prior. His batteries should have been well charged. I asked if he had been masturbating and he said that he can't because "it doesn't work anymore so I don't try." He is 53, but it is no problem for him to have sex twice, or even three times in the one day. He wants sex most mornings and often at night as well. Sometimes, he will have sex and then only a couple of hours later, will want more sex because he says "it makes it more intense."
I questioned why he needed to "recharge his batteries" and reminded him that we often have sex twice a day. He stared at me and said, "When did we ever do that?" ?????
I said... "What do you mean? We always do." and he replied, "No we don't." I can't understand how he can deny something that we often do... TOGETHER direct to my face, without even blinking and appearing totally genuine. It's like him suddenly insisting that we have never watched a movie together, even though we often do and watched a movie together only the night before. It makes no rational sense. My head hurts like my brain is doing nasty flip flops inside my skull. It's like pointing to his cat and insisting that it's a dog and always has been a dog and that I am a crazy person for ever imagining that it was a cat in the first place. I am feeling crazy just thinking about it.
My gut feeling is that he wasn't watching movies all day like he said when I was at the hospital with my son. He was having sex with someone, in our house, possibly even in our bed and certainly more than once that day, to the point where he felt that he wouldn't be able to go another round with me.
Why he said the recharging batteries comment, who knows? Maybe he wants me to know, but not challenge him on it? Maybe he sees the random women he has sex with (possibly including me) as "objects" to satisfy him and he gets confused about who he is with and when. (That sounds to me like a fairly out there explantion.)
The next day, I found a PINK ladies razor with BLOND hair in our shower. Needless to say, I am not blond.
Bottom line, I think I am crazy to still be here. I think he is seriously mentally ill, but that is no excuse for his disgusting behaviour. A part of BPD is random, unsafe sex with multiple people. He says he won't wear a condom and never has in any relationship except one. He admits to numerous "relationships" at least 15 that I know of, not including casual sex partners, of whom I gather, there are many. He has admitted to having relationships with multiple women at the one time on more than one occasion. He boasts about the fact that he could manage maintain a relationship with 4 or 5, all of whom knew about each other and were ok with it. He has told me intmate detail (in a boasting manner) of what he did with other women. Things I didn't want to hear, but listened to anyway. Things I have never done. Things that sound interesting, but that he refuses to do with me. I feel inadequate, boring and unable to please him. Prior to him, I had always been complimented on my looks and x rated abilities. I have even worked as a lingerie model.
He insists he has changed now and only wants me. He has deleted all social media and is not on dating websites or looking at porn (at least on his main phone). He does love me and has asked me to marry him.
I am afraid to outright ask what he is up to, or accuse him of cheating because of his potential to become physically violent.
I have tried telling him that I would be ok with the idea of exploring relationships with other people. He didn't buy it and is very jealous. He insists that life is behind him because he is too old for that now.
Really??? Opinions welcome.