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Playing in his first match since breaking down in tears during his return from injury last week, the Briton looked set to force a deciding set against Spain's Martin Landaluce.
But the former world number four spurned six set points as 20-year-old Landaluce won five straight games to clinch a 6-3 7-5 victory.
Draper, 24, finished with 47 unforced errors and 12 double faults against the world number 64.
He was playing just his second match since June having recently lost to Terence Atmane at the Canadian Open.
A persistent arm injury kept Draper sidelined and caused his world ranking to plummet from fourth to as low as 160th in a 12-month period.
Since injuring his shoulder at the US Open in August, Draper has struggled with bone bruising and pulled out of scheduled comebacks at Wimbledon and the Washington Open this summer.
While he did not appear to be injured against Landaluce, he tired during the second set and his confidence seemed gone once the Spaniard made it 5-5.
Draper has recently consulted biomechanics expert Carlos Cano in a bid to resolve his injury problems, with the 61-year-old Mexican having already helped Arthur Fery become British number one.
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