This is actually a very interesting question, as this play, plot wise, does not seem to have the normal structure of a text in having a character that is trying to achieve something that other characters are opposed to. In fact, Wilder seems to have produced a play that focuses on the normal cycle of human life and the way that death interrupts that cycle so often. This makes me think that the protagonist is not so much one character but all of the humans who are presented in this play, and that the antagonist is death, who cuts their lives short and ends their existence. Again and again the Stage Manager refers to the passing of time, such as in the following comment when he talks about marriage:
I've married over two hundred couples in my day Do I believe in it? I don't know. M ... marries N . . millions of them. The cottage, the g-cart, the Sunday-afternoon drives in the Ford, the first rheumatism, the grandchildren, the second rheumatism, the deathbed, the reading of the will,... Once in a thousand times it's interesting.
There is constant reference made to the cycle of life and what happens as we gradually grow up and get older. Without a traditional plot, it seems that the only antagonist in the play is the force of death that terminates our lives.