Is a "wandering eye" ok?

My boyfriend randomly talks to females over social media. He passes it off as "harmless" even if they are romantically interested in him and if they flirt with him. He never knows why he does it but begs me to not leave him. Is this normal or okay? I'll randomly find out every 3 or 4 months but it's like his 3rd chance at least. 
I find myself becoming more detached and I don't trust him. Why does he NEED female attention? Is he THAT bored to constantly need fun conversation? It's immature and ridiculous. What would you do? It's so hard for me to just leave because he's the first who I've found that accepts me for who I am and supports me through thick and thin.