Li, the second seed at Devonshire Park, got the news form her coach that French opponent Marion Bartoli, the 2011 winner, would not be playing their second-round match due to a viral infection.
"I have a virus and a fever and am really feeling terrible, I started feeling this way on Monday but it has gotten worse," said the unseeded Frenchwoman. "I'm hoping to be back on the court after a few days of rest to get ready for Wimbledon."
Li went back to the practice court after her free ride in the pre-Wimbledon warm-up event.
"This is not the best way to win a match. So I was feeling so sorry for her," said the former Roland Garros champion.
Czech Lucie Safarova put out Australian Samantha Stosur 7-6 (7/5), 6-3 while American qualifier Jamie Hampton followed up her defeat of top seed Agnieszka Radwanska by beating Hsieh Su Wei 6-4, 7-6 (7/2).
Raonic, playing as top seed on a wild card, will head to the Monday start of Wimbledon without a grass win after defeats in Halle and here.
The 15th-seeded Canadian has recently started working with former Croatian player Ivan Dodig but the combination has so far yet to bear much fruit.
Raonic admitted that he struggles on grass. "It's more me," he said of his problems on the surface. "I've got to figure out my thing.
"It's like I'm just not executing the things I need to execute.
"Obviously the surface doesn't make it easy. I think it's easier for me to figure out things on hard courts per se, but I think it's all on my shoulders."
The top seed lost serve twice in the opening set after losing the first game on a run of errors. The second was more competitive, but the Canadian came up short in the tiebreaker despite saving a match point.
"I don't think I'm a worse player, I don't think I'm playing worse," said Raonic. "I've been playing okay. But in the last few weeks I haven't played my best, That affects the confidence in those tight situations, and how you deal with them."
Feliciano Lopez of Spain upset Argentine fourth seed Juan Monaco 6-4, 6-4 while fellow Spaniard Fernando Verdasco reached his first quarter-final since Bangkok last September with a 6-4, 6-0 defeat of compatriot Albert Ramos.