So in the month you've been dating he's only been sober for a day or two?
there has been a day or so when he didn't drink
I do and I don't want to leave him and I hope he gets better
This relationship is only a month old. In this stage of the dating game you're usually on your best behavior, trying to impress your prospective mate. If this is how he's acting now it's only going to get worse down the road, when he's able to be himself and stop putting on a show to impress you, which he hasn't done.
After only a month you have nothing invested in this relationship. Leave now and save yourself the trouble. This isn't going to get better. You either accept him the way he is, or you leave. You won't change him, so if that's what you're hoping will happen, you're fooling yourself.
Good luck.