Ball catch type door closing mechanism

I have seen some roller type latches that work in the same fashion. You could always use flush bolts. Another option would be to use a spring-loaded hinge just to keep the doors in the shut position. Once you adjust the ball and get it to where it's working properly I would put a little clear nail polish on the side so it resists moving up and down when you open and close it rotating the ball down over time.

Was going to say this. Try to lubricate.

Assuming the height is adjusted correctly, use a little Vaseline on the ball