British No 1 Robson crumbled on her second serve on her way to a 6-3, 6-4 defeat to Daniela Hantuchova of Slovakia after Watson had already lost her match with Russia’s Alla Kudryavtseva.
Guernsey 21-year-old Watson was playing only her third match since coming back from glandular fever but rarely threatened on her way to a 6-4, 6-3 loss, and Konta’s subsequent 6-4, 6-1 dismissal by French 12th seed Kristina Mladenovic left Britain without a player in the third-round draw.
World No 5 Hantuchova took advantage of Robson’s faulty second serve to book herself a clash with Mladenovic in the next round.
Robson, 19, won just seven of 26 points on her second serve, compared to 92 per cent on her first, but her early exit will allow her extra time to prepare for Wimbledon with new coach Miles Maclagan.
Kudryavtseva is ranked 118 places below Watson but the qualifier raced through the first set before quickly building a 5-2 lead in the second by breaking the Briton three times. Watson did prevent her from serving out but, having only claimed 42 per cent of points on her second serve, ended the match with a double fault. Australia-born Konta, meanwhile, struggled against Mladenovic, who had beaten British number four Tara Moore in the first round.
There were also victories for third seed Sorana Cirste of Romania and German fifth seed Sabine Lisicki, who beat Tsvetana Pironkova of Bulgaria 6-4, 6-4 and Czech Kristyna Pliskova 6-4, 6-2 respectively.
Serbia’s Bojana Jovanovski saw off Czech Andrea Hlavackova 4-6, 6-1, 6-4 and Croatia’s Mirjana Lucic-Baroni triumphed 6-4, 6-0 over Belgian Yanina Wickmayer. American. Maria Sanchez defeated another Belgian, Alison Van Uytvanck, 7-6 (7/3), 6-3 win before rain delayed evening play.
Russian second seed Ekaterina Makarova might have hoped the weather had washed the rest of the day’s play away as she suffered a 7-6 (8/6), 3-6, 6-0 defeat to New Zealand’s Marina Erakovic after the restart.
Francesca Schiavone of Italy joined Erakovic in the third round by beating Ukraine’s Nadiya Kichenok 7-6 (7/4), 6-2 and Slovak Magdalena Rybarikova defeated Mathilde Johansson of France 7-5, 6-7 (4/7), 6-4.
The night’s last match was an epic encounter between Kirsten Flipkens and Croat Ajla Tomljanovic – and it was the top-seeded Belgian who finally found the extra push that she needed to go on to seal a 4-6, 6-4, 7-5 victory.