Failure is, arguably, a relative concept in Death of a Salesman. While Willy Loman clearly fails in his own eyes to achieve his dreams of wealth and great success, he does manage to pay off his mortgage and raise two children. The fact that Biff ultimately comes to mature morally and learns to accept himself with humility and honesty suggests that Willy has not completely failed as a father.
The successes that Willy does achieve are rather subtle in comparison to his visions of grand success along the lines of that achieved by his brother Ben, who makes a fortune through daring and adventurous investments in exotic places (Alaska and Africa).
"Uncle Ben, Willy’s brother. He goes out into the jungle and in a few years returns from the diamond mines a rich man. His success is an accusation to Willy" (eNotes).
In Willy's delusional conversations with Ben, we see that Willy once had high hopes for himself and for his sons. Ben's great success becomes a standard for Willy - one that he fails to to meet.
Notably, Willy is engaged in a series of lucid memories wherein he remembers and re-imagines the past. In these episodes we see his pride in Biff and his belief that Biff can be a great man one day. We also find Willy mis-remembering Biff's role at the sporting goods store when he suggests that Biff was once a salesman there.
Biff: [...] How the hell did I ever get the idea I was a salesman there? I even believed myself that I’d been a salesman for him! And then he gave me one look and—I realized what a ridiculous lie my whole life has been.
Willy's memories demonstrate his ideas of success and at times present a contrast to his current state. At the time the narrative takes place, Willy feels that he has not attained a level of respect at his job or helped to launch either of his sons on a path toward financial (or moral) success.
Thus Willy's memories of Biff's glory on the football field and his mistaken memory that Biff was an up-and-coming salesman at the sporting goods store become indications of the type of success that Willy had hoped for - for himself and for his sons.
In certain moments, Willy insists that he is or was once known as a great personage and a fine salesman across the east coast. This too is a depiction of the success he sought - to be respected and well-liked, to be a potent figure.
In identifying Willy's hopes and dreams and marginal success (in his own eyes) in the past through flashbacks and recollections, the play effectively suggests that Willy's failure has occurred some time between the past and the present. The intervening years have been years of decline, leading Willy to despair, bitterness and rancor.
Despite the humble achievements he has made, Willy has not won the day as his brother did and as he hoped his son Biff would. Importantly, Willy's failure is not absolute. His failure is arguably one generated and demanded only by his own perspective.
Had Willy come to an epiphany like Biff's wherein he was able to see himself clearly, perhaps Willy would have understood what Linda was trying to tell him and could have found some peace.
"Willy struggles with the image of his ideal self his entire life, until he can no longer deny the fact that he will never become this ideal self and he commits suicide" (eNotes).