Popzie. On a very basic level, what you are saying is that you have a large need that is being unmet. In any relationship, having such a big need unmet will cause problems in the future, not least when someone comes along who appears to meet that need. I do think there are some people for whom a lack of tenderness and intimacy would not be a problem - but you always knew you weren't one of them. And I suspect that the vast majority of people share the need for intimacy and connection in their romantic relationship - I know I do.
However, on an ethical level, you always knew that your H wasn't like this and therefore it would be terribly unfair to him if you were to get involved with someone else. You are showing great foresight in realising that you are vulnerable and so here's what I think you could do.
You say you have explained and advised to your H about this need - and he says he cannot do it. However, I wonder whether you have explained yourself as clearly as you have in your post - it could be that you need to change the conversation. I think a lot of couples have these "groundhog" day conversations that are in essence the same each time - and find that nothing changes. If every time we do something, the same unproductive result occurs, it follows that we need to change what we are doing. In this case, it means you need to change the conversations you are having about this matter.
I wonder whether he has always been like this in his previous relationships - did he ever show tenderness and imtimacy with partners? Could it be that he did once and got badly hurt, therefore he surrounds himself in a sort of protective shell? If someone was unfaithful to him before, this often happens. Unfortunately, this behaviour then becomes a self-fulfilling prophesy that infidelity will happen again.
What was his childhood like? Was affection and sentimentality frowned upon in his family? It takes many years to unlearn the lessons absorbed in childhood.
I think counselling would really work for you and in this case, some on his own might help, as well as some couples counselling.
In your shoes, if you are able to tell us that his behaviour has been learned because of earlier hurts - either in childhood or a previous relationship - my approach would be to reassure him that you would never be unfaithful to him, but that you do need change - and that if he cannot do that, you might have to part. I would say that you realise that many people in your situation go down the affair route, but you have far too much respect and love for him (and yourself) to do that. He should therefore regard this honesty from you as a great gift.
I would say that you have realised that you cannot go on without intimacy and connection and that it is a really big deal to you - you cannot be happy with him without it in fact. You don't want to leave the marriage and would like him to work with you on this - and go to counselling. Be very firm on this - he should be left in no doubt how serious this is and how imperilled the marriage is. He needs to wake up and see the need for change.
On the other hand, if he still insists he is "just like this" and incapable of change - and cannot (or will not) trace this behaviour back to an earlier event, then you have to decide whether you can live with him as he is. If you feel you cannot (and I couldn't) then all I would say is, please do the ethical thing and end the relationship rather than waiting for an affair opportunity to present.