Trust is essential to a relationship. I don't question your love for each other but IMO without trust there isn't real love.
As for your situation if you do want to hold on to this man and do see a future with him you can suggest therapy for him to get to the bottom of his issues. If he is willing to go through with it you can stick with him or suggest breaking up at the point and then evaluating things down the track. It sounds he could take a while to 'fix' though which is uncertain and unsettling for you as you may hang around and wait for him with no guarantees he will change. This could prevent you from potentially meeting someone else in the meantime.
It is a difficult situation however it really is up to him to make the changes required for you both to have a healthy relationship. He needs to understand this.
Some people are drains and some are radiators... Keep clear of the drains and hug the radiators!