It ends the tournament for Augsburger and the Valencia-born Rico, who took the in-form Di Nenno and Stupaczuk to the tie-break in the second set but could not force a decider.
The two other Valencians still alive, Edu Alonso and Juanlu Esbri, saw their tournament also come to an end on Thursday at La Fonteta against Jon Sanz and Alejandro Galan.
In what will be their final tournament together, Sanz and Galan will look to make their first final and are now just two rounds removed.
Watch all of Thursday's centre-court highlights in the video below!
Matches in chronological order:
Martin Di Nenno / Franco Stupaczuk (2) vs Javi Rico / Leandro Augsburger
Jon Sanz / Alejandro Galan (3) vs Edu Alonso / Juanlu Esbri
Arturo Coello / Agustin Tapia (1) vs Juan C. Belluati / 'Coki' Nieto
