Can a man become infertile after having two children?

It depends on why he is infertile.

Since he already has two children it is apparent that he doesn't have a congenital infertility, but there are many types of infertility that can occur during a person's life. I would ask him why he thinks he is infertile. If he can explain a particular event then he may be infertile, if it is just cause he has had lots of sex and not gotten anyone pregnant, then it could still be fertile.