Yes, the old man in Earnest Hemingway’s short story “Old Man at the Bridge” was about to give up on his life. It is quite evident both in the narrator’s comments and from the old man’s own speech.

The readers start thinking the same when the speaker says —

There were not so many carts now and very few people on foot, but the old man was still there.

Everyone was going away from the place as the enemy forces were approaching, but the old man was still sitting there. It can only indicate that he was bot only helpless, but also hopeless. He probably gave it up.

I was the last one to leave the town San Carlos.

I have come twelve kilometers now and I think now I can go no further.

…got to his feet, swayed from side to side and then sat down backwards in the dust.

All the above quotes refer to the same hopelessness and exhaustion the old man was in.

There is no need to be unquiet about the cat. But the others. Now what do you think about the others?

When the old man repeatedly expresses his concern for his pets and not for his own life, it only signifies that the man gave up hope of his survival.