Eugenie Bouchard of Canada has been knocked out in the first round four times in her last 10 tournaments. (Clive Brunskill/Getty Images)

Eugenie Bouchard threw down her yellow racket on center court Tuesday during her first-round match at the Citi Open. The Canadian had already lost the first set, and Italy’s Camila Giorgi had just taken a 4-2 lead in the second set. Bouchard’s hopes were dwindling. Giorgi took the next game, too, while holding serve to take a 5-2 lead.

Bouchard didn’t give up, winning the next two games of the second set to reduce Giorgi’s lead to 5-4. But it still wasn’t enough.

The 7-5, 6-4 defeat marked the fourth time Bouchard has lost in an opening round in her past 10 tournaments. Bouchard, who is ranked No. 41 in the world, hadn’t appeared in the Citi Open since 2013, when she was eliminated in the first round by Ekaterina Makarova in two sets. She and her doubles partner, Taylor Townsend, placed second that year.

Bouchard’s best singles outing in the Citi Open came in 2012, when she advanced to the quarterfinals before falling to Sloane Stephens, 6-4, 6-4.

Bouchard hasn’t yet confirmed whether she’s playing in next month’s Olympics in Rio de Janeiro, Tennis Canada President and chief executive Kelly Murumets said at a news conference in Montreal ahead of Tuesday’s match.

“I know that she wants to play the Olympics and she’s been part of our campaign and she’s wearing the Canadian flag on her heart,” Murumets said, according to the Canadian Press. “I think the health concerns in Rio are scaring her a bit, so I think she’s a little bit on the fence.”

Bouchard is Canada’s premier women’s singles player and is entered to play in doubles as well, with Gabriela Dabrowski.

Bouchard maintained that she has not made up her mind about going to Brazil and cited concerns about the effects of the Zika virus.

“I am trying to learn as much as I can about it. I don’t know if anyone knows enough about it to really give a good opinion on whether, as athletes, we should go or not,” Bouchard said. “I don’t know if the health of my future babies is worth it. That’s what I’m trying to decide in my head. I’m truly undecided.”

Something to build on

American Christina McHale faces the tall task of needing to follow up on a near upset of Serena Williams at Wimbledon, but a win in the first round of the Citi Open could be a start. She beat Monica Niculescu, 6-3, 6-4.

McHale’s serve was the key to getting her into the second round.

“It’s just the culmination of all the hard work I’ve put in,” McHale said. “It’s been up and down. It’s a process. I’m putting myself in more opportunities to win, and if I keep at it, hopefully it’ll keep going.”

Her third-round loss to Williams in London — after winning the first set in a tiebreaker — helped build McHale’s confidence. There is, however, one thing she hopes will change.

“I want to stop meeting [Williams] early in tournaments,” McHale said with a laugh. “Those were fun ones.” . . .

Irina Falconi of the United States was looking for answers after losing to Naomi Broady of Great Britain, 6-3, 6-4. She repeatedly pounded groundstrokes into the net in her first-round loss.

“I would just miss them and was like, ‘What is going on with you?’ ” Falconi said.

Falconi, an Ecuador native who is ranked 70th in the world, is still working to get back in rhythm after an injury suffered ahead of the French Open set her back. And despite her subsequent struggles, Falconi said her support system is helping her maintain her confidence. . . .

Grigor Dimitrov, ranked 40th in the world, fell to No. 82 Dan Evans of Great Britain, 6-4, 6-0.

The Bulgarian was down 3-1 early in the first set and was unable to rally.

“I was not playing good tennis,” Dimitrov said. “Missing a lot of balls. Focus wasn’t good at all.”