Frankly, I think it *is* big enough to end a relationship over.  Not necessarily because of the communication, but because you have made it crystal clear to your partner that you don't like it and can't live with it and he is not willing to put up boundaries for you.  If it's not this, it will be something else.   

His excuses are pretty flimsy.  I'm not sure I would end a relationship over this, if this is the only issue the two of you have.  BUT if he behaves similarly in other areas - doing what he wants knowing that it bothers you - it's going to be a long, difficult slog.

Well, I hate to break it to you, but it's either big enough of an issue to end the relationship or it's a small enough issue that you have to disengage and not care anymore.

Your BF isn't interested in meeting the standard you are wanting to set. Your BF has made his decision about what he's going to do, and that means the ball is back in your court to decide how you want to proceed.

You can try to find a new compromise with him and move your line closer to his. Or, you can move your line to his and accept what he is comfortable with. Or, you can erase the line completely and disengage from it. Set your own boundaries (like leave the room if he gets into a text frenzy, sleep on the couch if she calls in the middle of the night, leave dinner if he feels to chime in on date night). Disengaging isn't the same as ignoring; it's doing what you need to do remove the stress of the situation, usually by removing yourself because you can't remove the stimuli.

Or, you realize that this is not how you want to live, and you take an entirely different path than the one you're walking down. You can end the relationship.

However, living in a state where you're mad and can't/won't move forward isn't good. You either accept the situation for what it is or change the one thing you can control - you. You're not going to be able to make your BF do what you want him to do; you can only make your decision and toss the ball back to him to decide his next move (or kick the ball down the street because you're done playing).

There's a difference with being "flexible" and basically BM having him by the b@lls and controlling his every move. Since he's never enforced strong, proper boundaries and remain consistent she feels she gets to do as she pleases and to hell with respecting his time and space. He has the power to shut this down and have one major way for contact but his fear doesn't allow it.

She will continue to rule his life and how he chooses communication because he allows it. I'd be annoyed by this to and will let him know that this shit show is tiresome and one day I won't be around to continue to see another woman have his balls in her purse.

I personally think that not maintaining appropriate boundaries in your home and in your relationship is a big enough issue to end a relationship over. This is about BM wanted to show everyone that she is still in control of what your BF does, not you. 

He's okay with her being in control, which means he hasn't made space in his life to have an actual adult relationship. 

If there was a true emergency, the police could find him. 

Dealing with people without boundaries is difficult. My DH has finally set boundaries with BM and it basically cost him his relationship with his family because they now tell him that he's "not nice enough" to BM and "not respectful enough to her". None of them ever weighed in when BM was screaming at DH in front of the kids. His family also lacks healthy emotional boundaries and that was a struggle, too. 

I think at this point, you have to decide if you're okay with your BF's behavior or tell him you're done. He won't change unless he faces some real consequences...and even then, he might not change. 

If it's been like this and you've already made it clear that it bothers you and he has done little to nothing about it, it probably won't change. Or he may just become better at hiding his communication with his ex.  He is the one that isn't respecting your guys relationship. She is only doing what he is allowing her to do. It takes two to communicate, and the moment she starts talking about things that aren't related to the child then he needs to stop replying. I think if it's causing more pain then it is worth ending a relationship over. I had the same problem you had at one point. He would do everything you described. I brought it up and told him it bothered me. Instead of fixing it, he just got sneakier about communicating with his ex while I wasn't around. I wish I would have ended it a long time ago, but I didn't think it was a big enough issue at the time. But IT WAS! Well it should have been for me anyways...