Italy’s Paolo Lorenzi beat Müller 6-7 6-3 7-6 6-3 in a 3:28 men’s singles match on Wednesday.
Lorenzi will go on to face fellow Italian Thomas Fabbiano in the third round.
Müller had notched up a win during his first foray at the tournament, on Monday 28 August.
He beat Australia’s Bernard Tomic 3-6 6-3 6-4 6-4 in a 2:33 match.
In July, Müller made it into the quarterfinals at Wimbledon, losing to Croatia’s Marin Čilić.