Tennyson's poem "Tithonus" is told through the view of the title charcter. In Greek mythology, Tithonus was a mortal man with whom Eos, the goddess of dawn, fell in love. According to the ancient myth, it was Eos who asked Zeus to make Tithonus immortal. In Tennyson's poem, however, it is Tithonus who makes the request ("I ask'd thee, "Give me immortality.") and it is Eos, not Zeus, who grants the request.
In the ancient story, Eos forgets to ask Zeus to also grant Tithonus eternal youth; Tennyson is unclear whose responsibility it was to ask for eternal youth. In either case, the result is the same: Tithonus lives forever, but keeps on growing old. In the myth, Tithonus eventually shrivels away until only his voice is left. Then, some sources have him change into a cricket.
Tennyson's poem stresses Tithonus' decay into old age and wishes the goddess could take back her gift ("take back thy gift"). He wonders why anyone would want to live beyond the lifespan that is customary for humans. Unforunately for Tithonus, "The Gods themselves cannot recall their gifts", and so Tithonus lives on.
He recalls the pleasure he had with Eos when he had his youthful appearance, but in the poem's final 12 lines he knows that he is wasting away and that she will eventually see him dead.
So, whereas Tithonus recalls the pleasures of his youthful association with Eos, his growing old while she remains forever young is painful to him.
Apparently, Tennyson wrote the first version of this poem after the death of his friend Arthur Hallam in 1833. Tennyson himself was a young man in his mid-20's at that time. Tennyson released a second version of the poem in 1860. So, just as Tithonus recalls his youth and laments his old age, Tennyson originally wrote this poem as a young man, but the final version that we have was written when he was in his early 50's.