(CNN) -- Victoria Azarenka edged closer to a quarterfinal clash with U.S. Open champion Samantha Stosur at the French Open but 2002 finalist Venus Williams followed sister Serena out of the Paris tournament Wednesday.
Venus, a seven-time grand slam champion, has struggled with illness all season after being diagnosed with Sjogren's syndrome, an incurable condition that affects energy levels and causes pain in the joints.
And she was beaten 6-2 6-3 by Poland's No. 3 seed Agnieszka Radwanska to end any hopes she had of adding the French Open to her list of major titles.
"This is just the beginning for me. Again. I have to be positive when I walk out on the court," she was quoted as saying on the tournament's official Twitter page.
"I'm not playing under ideal circumstances but at the moment it's about improving Olympic chances so I'll deal with this somehow."
As for her sister's exit on Tuesday, Venus added: "Thankfully (Serena) has 20-something majors to keep her warm at night so she'll be alright."
Radwanksa will now face Russian No. 26 seed Svetlana Kuznetsova after she beat Yung-Jan Chan from Chinese Tapei.
Azarenka, the world No. 1 showed no signs of struggle in her victory German qualifier Dinah Pfizenmaier 6-1 6-1, unlike her first round scare against Alberta Brianti on Monday.
The 22-year-old took just under an hour to defeat Pfizenmaier, who was competing in her first grand slam tournament, and had joked prior to the match that her opponent might not remember her name.
"I never knew her before but I had to do a little bit of research yesterday, and I do remember her name -- it's just a little bit difficult to pronounce!" Azarenka told the WTA Tour's website.
"Now I know what she looks like, so hopefully I will see her many more times. It took me a few games to understand what kind of game she plays, but after a few games I started to find my rhythm. I definitely played better today.
"I remember myself, the first time I passed the qualifying at the French Open I was 16 years old -- I was up, 6-0 3-1, and I lost the match 9-7 in the third set.
"I think she has big potential. She has good shots. I think she did really well today. She has a good game, so hopefully she has a good future."
Azarenka, from Belarus, will now face Aleksandra Wozniak of Canada after she beat the No. 31 seed, Jie Zheng from China, 6-2 6-4.
Stosur wasted little time in negotiating her way past Irina Falconi of the United States, winning 6-1 6-4. She will now face Russia's Nadia Petrova after the No. 27 seed beat Chanelle Scheepers, from South Africa, 6-3 6-3.
"It's still only the third round and there is a long way to go yet before you are holding the trophy," Stosur said.
"I think it's just one of those things -- you have to knuckle down. I know that I've had good runs here in the past. Now I'm up to the third step of that."
The shock of the day sent a home favorite out as No. 8 seed Marion Bartoli, was beaten 6-2 3-6 6-3 by unseeded Croatian Petra Martic.
Lucie Safarova, the No. 20 seed from the Czech Republic, was also ousted from the tournament, beaten 6-4 7-5 by Spain's Maria Jose Martinez Sanchez.
The 2008 champion, Ana Ivanovic, seeded 13, made light work of the challenge posed by Israel's Shahar Peer, winning 6-2 6-2.
No. 15 seed Dominika Cibulkova of Slovakia beat Vania King of the United States 6-0 6-2 while Italy's Sara Errani, the No. 21 seed, defeated America's Melanie Oudin 6-2 6-3.
There was a defeat for the No. 24 seed Petra Cetkovska, from the Czech Republic, as she slumped to a 7-6 6-2 reverse to France's Mathilde Johansson.
Flavia Pennetta, the No. 18 seed made it into round three. The Italian beat Alexa Glatch, from the United States, 6-3 6-1.