Bogdanovic had to come through qualifying in Eastbourne
British number two Alex Bogdanovic suffered a narrow defeat by second seed Dmitry Tursunov at the Aegon International in Eastbourne.
The Briton, 25, led 5-3 in the final set tie-break before the Russian hit back to win 6-7 (2-7) 6-4 7-6 (7-5).
James Ward suffered the same fate as his compatriot as he was beaten 7-6 (8-6) 6-4 by Canada's Frank Dancevic.
Tursunov is the highest seed left in the draw after Igor Andreev lost to Dancevic on Tuesday.
Bogdanovic, ranked 189, had break points in game eight of the final set but Tursunov remained solid on serve, and Bogdanovic then netted a forehand when 5-3 up in the tie-break before Tursunov reeled off the next three points for victory.
It could have been anybody's match and I think I can take a lot of positives from it
"It's tough to lose like that, pretty tough," said the 25-year-old from Middlesex. "In the second set my first-serve percentage was down. I missed a lot of first serves and he attacked my second serves which gave him the break.
"You have to serve pretty well against players like that because as soon as your serve dips a bit he's going to jump on it. It could have been anybody's match and I think I can take a lot of positives from it."
Tursunov said: "He's a difficult guy to play, he's got all the shots and it was definitely tough. I definitely think he should be ranked much higher than he is because he's got all the tools, he just needs to put everything together."
Ward was another disappointed Briton after losing to Canadian qualifier Dancevic.
"I felt like I was the better player out there in the first set," said the British number four. "My level dropped a bit in the second set and it was frustrating because it was a winnable match."
Elsewhere in the second round, sixth seed Sam Querrey was knocked out after losing 3-6 7-6 (7-3) 6-4 to Denis Istomin of Uzbekistan, while Argentina's Leonardo Mayer beat Julien Benneteau of France 6-4 6-4.
In the women's draw, world number four Elena Dementieva joined the exodus of top seeds when she was beaten by Virginie Razzano.
The Russian number one seed was the only one of the top four to reach the second round but got off to a terrible start and eventually lost 6-0 3-6 7-6 (7-4).
Razzano will now face eighth seed and defending champion Agnieszka Radwanska, who was the beneficiary of last week's Aegon Classic winner Na Li's retirement when 1-3 down in the opening set.
French Open semi-finalist Samantha Stosur could not repeat her Paris form as she lost 6-1 5-7 6-1 to Danish sixth seed Caroline Wozniacki - who the Australian had beaten at Eastbourne last year.
France's Amelia Mauresmo lost 7-6 (10-8) 7-6 (15-13) to Ekaterina Makarova of Russia, and seventh seed Nadia Petrova retired in the second set against compatriot Vera Dushevina.
In the doubles, Britain's Jamie Murray and Israel's Jonathan Erlich lost the champion's tie-break that decided their first-round match against Bruno Soares and Kevin Ullyett, held over from Tuesday night, 4-6 7-6 (8-6) 10-7.
"The match was OK but to lose is disappointing," said Murray. "I started to feel better in the last couple of weeks but obviously getting the wins on the board is the most important thing though and that's not happening.
"Today was a wipe out but we played well yesterday so I feel OK going into Wimbledon."
Wildcards Sarah Borwell and Anne Keothavong lost their second- round doubles match 7-6 (7-3) 6-3 to Akgul Amanmuradova and Ai Sugiyama, and Soares and Ullyett defeated Colin Fleming and Ken Skupski 6-3 6-7 (5-7) 10-7 in their second-round contest.