Forget that "drunken mind speaks a sober heart" shit. When you're drunk, you're not completely cognizant; liquid courage cannot be trusted. If you're intoxicated and you break things off, your girl won't take you seriously. Even if she does, you won't remember anything you said to her the next day, and she definitely isn't going to be the person to remind you. Dump her when you're sober so she knows it's real.
When You Are Drunk