My boyfriend dumped me twice and cheated on me twice in our serious 3 year relationship, he wants to win me back. My trust is gone, should I stay and try to build the trust again or is it a lost cause?

Find someone that treats you well, you owe yourself that. Don't let this man treat you this way, kick him to thd kerb. Because the trust has gone, the whole time you stay with him you will fear he is cheating. He wasn't thinking about you while he was with these other women he was thinking about himself.  While you remain with this man you are telling yourself that "this is all you deserve," and you're missing out on that fantastic man who's waiting to meet you, love you and treat you right. So love yourself and leave him.

I'll leave this song that got me through my first break up after a 4 year relationship; -

https://m.youtube.com/watch?v=NgTuPoNfAAc

Lost cause.  He is a cheater.  He has proven that. He will cheat on you again.  Of course he wants you back.  Players like him want as many conquests on their string as possible.  Girls who keep taking them back no matter how bad they are treated are like bonus points for players.  Stop letting him play you.  Have enough self respect to tell him to take a hike instead of believing whatever lies he tells you. 

Honestly he is an A**hole. Cheating once it could be acceptable (I am not saying it is accepted) but depends upon how were your relation before but doing the same mistake twice??

Are you kidding? He just want to use you. Wait sometime, someone will be there for you. Just give yourself sometime.

More than likely he will do it again. I'd move on and find someone that I could trust.

He's not worth your love or trust. Leave him in the gutter.

Fool me once Shame on YOU . . . Fool me twice? It is I THE FOOL!

Yes, I changed it to fit the scenario . . .

The Impulsive nature of a man takes years to hone . . For good or bad, it is theirs alone.

Whilst they may seek good works and dare to atone . . . The evil they will do, is their heart's only home.

I was in a rhyming mood this morning . . Who'd have thought.

Once Trust is gone, rebuilding it always finishes with a weaker result . . . If you haven't already, you will find the foundation of this relationship to be more and more "shifting sands" and less that made of solid stone.

Time to walk away . . .

Honestly I think you should take some time for yourself. Definitely don't bother with him ever again but also wait a little bit before jumping into another relationship. Get to know you better. Find out what you're willing to bring to a relationship and what you want in return. Because believe it or not this relationship has changed you in ways you probably aren't even aware of yet. Also starting a new relationship too soon could be the beginning of a big disaster. I'm sure you still have pain from your ex and the trust issues will only make things worse. You need to rebuild yourself. You don't want to enter into a new relationship and end up making them pay for your ex's wrong doings. Make sure your wounds are healed inside before dating again. Good luck.

Well, the choice is up to you.

But how many more times do you want to go through this again.

He shows no real interest in changing---either your relationship is more like a game with him or he thinks his behavior is (at at least some level) acceptable to you.