What is the significance of the painkiller requested by Hamm?

Throughout the course of the play, Hamm asks
five times, Is it not time for my pain-killer? The first four times he asks, his servant Clov
tells him, with increasing anger, that no, it is not time for his pain-killer. The fifth time he
asks, Clov tells him that it is time, but that there are no more pain-killers and that he will
never get anymore.

In response, Hamm asks, at first pitifully and then
again In a scream, Whatll I do? His response indicates that he will be unable to carry on
without his pain-killers. They make life bearable for him. The prospect of living or trying to
live without them makes him feel desperate, lost, and hopeless.

Hamm is
elderly, blind, misanthropic, and miserable. He suffers physical pain, but he also endures a
sort of existential pain. In other words, the endless and insufferable meaninglessness of his
existence causes him great and inescapable anguish. Indeed, he is, in his own words, no more
than a speck in the void, surrounded by Infinite emptiness. By having Hamm repeatedly ask
for his pain-killer, Beckett is emphasizing the extent and degree of the pain that he suffers,
both physical and existential.

Hamm is also of the opinion that the pain he
suffers is worse than any pain anybody else could possibly suffer. Arguably, therefore, the
repetition of his request for his pain-killer serves not only to emphasize the intense pain and
suffering that Hamm must endure but also to highlight how desperate and self-pitying he has
become.