How do you convince your partner to seek help if he doesn't recognize his problem?

It's not easy. One suggestion I can give you is to buy a book on the subject, whatever the problem is, and leave it around where your partner can see it. Don't put any pressure by asking your partner to read it, but leave it where it can't be missed. Maybe you could put a small mark in it, like a hair on page 50, so you could see whether or not your partner did look at it. If your partner is at least thinking about it, you might have an easier time getting him or her to go for further help.