Draper reached a career-high ranking of four in 2025 but had to cut short the season with a bone injury in his arm and also dealt with a knee injury this year.
He returned to action at the Canadian Open following his withdrawal from Wimbledon in June, breaking down in tears during his first-round loss to Terence Atmane.
In Cincinnati, Draper led 5-2 in the second set but Landaluce reeled off five consecutive games to win.
"The way I'm usually able to fight for every ball and conduct myself, it's just missing," Draper told reporters.
Draper is ranked 143rd and his early exits from Montreal and Cincinnati mean he will likely have to come through qualifying at the US Open, where he was a semi-finalist in 2024.
"The level of my fall almost from where I was last year and the amount of things that I'm having to change in my tennis ... The mountain seems very, very big," the 24-year-old said.
The US Open begins on August 30.