In the ending of Fate/stay night: Unlimited Blade Works, Saber and Archer chose to fade away rather than staying in the real world with Rin and Shirou.
This is one of the most confusing things for me to understand. I just can't get a grasp on this and have searched and thought about it for very long.
Why did they choose to fade away?
Because they can't stay in the world without a Master and the Holy Grail.
in the Visual Novel for the Unlimited Blade Works route, in the Good Ending Saber remains in the world through her contract with Rin, however Rin notes that it's a hassle to keep Saber in the world because the Holy Grail is no longer providing support.
It is possible to remain materialized as a normal familiar after the Holy Grail War ends, but it greatly increases the cost without active support from the Grail. Rin Tohsaka, a superior magus, has no issue in providing for Saber's upkeep, Noble Phantasm usage, and Shirou Emiya's Reality Marble at the same time during the Holy Grail War, but in-turn requires the majority of her energy and Shirou's help in keeping Saber materialized after it ends in Unlimited Blade Works.
Source: Servant > Nature > Upkeep (Last Paragraph)
for Archer, because he has the Independent Action Class Skill he can remain without a Master when normally a Masterless Servant fades away too. he became Masterless after Caster was defeated as Caster's Rule Breaker severed the contract between him and Rin (apart of his plan to go after Shirou) and Shirou did not kill him during their fight
Gilgamesh has this same ability but it's on a higher level that Archer's and was also boosted unnaturally by the Black Mud from the Grail thus allowing him to continue to be materialised after the 4th war and into the 5th with Kotomine using the Orphans from the resulting fire from the 4th war as a way to replenish Gilgamesh's energy (Shirou discovers this in the Fate Route)
Also both Saber and Archer felt they were no longer needed and leaving everything to Rin. in Saber's case it was simply not having a role in Shirou's life while Archer it was trusting that Rin would stop Shirou walking down the same path that he walked
