While there are different ways to answer how and why Usher's mind deteriorates, it is essential to focus on one specific aspect to establish what his decaying home truly represents, as a metaphor.
Hence, the best way to correlate the loss of Usher's mental faculties and the loss of his house's lustre, is by arguing that both losses are caused by the Gothic inevitability created in Usher's cursed bloodline.
This information comes from the narrator, when he confesses a discovery that he has made on the Usher clan.
I had learned, too, the very remarkable fact, that the stem of the Usher race, all time-honoured as it was, had put forth, at no period, any enduring branch; in other words, that the entire family lay in the direct line of descent
Here is an important piece of information: the Ushers are incestuous for whatever reason. This immediately reminds the reader of a mortal sin. The narrator tells us that, in his opinion, this may very well be a correlation between the Usher deterioration and the deterioration of the House of Usher, itself.
It was this deficiency, I considered, while running over in thought the perfect keeping of the character of the premises with the accredited character of the people, and while speculating upon the possible influence which the one, in the long lapse of centuries, might have exercised upon the other.
The idea of a deteriorating estate and a dwindling bloodline combines with a deep state of melancholy caused by both isolation and fate. These are the richest and most evident Gothic traits of "The House of the Fall of Usher". In Gothic literature, it is fate which dictates the beginning and the end of things. For this reason, the Usher's are certainly a cursed bloodline whose doings from the past have earned the deterioration and the extinction of their name, and their estate.