After an adulterous affair, begging the guilty party to stay is never a good idea; it feeds their ego and makes them complacent.
If you don't want him to pity you, don't be pitiable.
It may seem as if the 3 counsellors treated you harshly but, as each of them has effectively reached the same conclusion, it is probable that your childhood experiences have contributed to you being emotionally needy.
The hurtful truth is that you are only living with your h now because the other woman rejected him. What do you think he would do if she snapped her fingers at this late date? Despite what he has told you, I've got a feeling he'd go running.
Personally I'd have booted him out long ago. If that was not financially viable, I would have moved him out of my bedroom, made it clear to him that I intended to live my own life, and filed for divorce while we were living under the same roof. Those options are open to you.
If you want to break the negative cycle that is currently sucking the joy out of your life, stop pleading with him for love/sex and start looking at ways in which you can build your self-esteem and find an inner happiness that is not dependent on him.
In order for others to love us, we must first be loveable and that begins with loving ourselves. Ask your GP to refer you for counselling so that you can begin to resolve any issues around self-worth which have led to you defining yourself through your relationship with him.
In the meantime take good look at yourself in the mirror. Is it time you updated your 'look'? New hairdo/colour? Modified/altered your make-up? Enlist the help of a girlfriend and ask her to give you a frank assessment of what you need to do to show off and draw attention to your best features.
Find a couple of hours every week to pamper yourself. Relax in the tub with scented candles, exfoliate, defuzz, slather on the body cream, pedicure, mainicure. Do things that make you feel good - and do them for YOU.
You haven't mentioned whether you are working but, regardless, find an interest that you can pursue outside of your home. Evening classes, amateur theatre group, book circle, local government meetings (your town hall will have the details of the various committees together with dates/agendas).
Don't tell your h of your plans; on the appointed night be dressed up ready to go as soon as he arrives home and simply say 'I'm off to a, be or c, your turn to feed the dc/walk the dog/ etc, See you later', leave the house - and don't rush back.
If you are a SAHM sharpen your mind on current events; read newspapers online and pick an article to reflect on in depth before forming your own opinion, join in a m/net debate, listen to radio 4. Give your brain cells some exercise everyday - apart from anything else, this will stop you thinking so much about your trials and tribulations.
If you adopt these tried and tested ways of moving on after the heartache of finding out that the h you adored is little more than a lying twunt, you will find that you can function perfectly well without him and you may discover that he needs you far more than you need him.
If you know nothing else, know that he is NOT your best friend - YOU are.