I just want to offer some sympathy.
My dh is a lot like yours. Based on what he ate the night before, he waffles back and forth between yes and no to a third, and time keeps passing.
Ds and dd are 5 and almost 4, and I really wanted the third to be a lot closer together than this.
We have huge arguments about it about every three months. And he is also militant about protection and not having sex when it's risky.
Right now, he thinks he wants another one, but my period is currently wacky, so that's not helpful. He'll give it one shot (literally) when he thinks he wants another one, and then if I don't get pg, he decides it wasn't meant to be.
I've had enough, and I told him I want to TTC in October. Right now, he's saying okay, but I think it's just because it's three months away, and he figures he can talk me out of it.
He knows I'm not going to give up until I get my third, but he is fighting it all the way. My advice is to just keep bringing it up, because it is so important to you. You'll wear him down.