Published: Sep 25, 2011 2:55 PM EDT

MIAMI (AP) - Endurance athlete Diana Nyad soldiered on despite a painful jellyfish sting to the face and kept up her swimming ultramarathon Sunday, about halfway through a grueling course from Cuba to Florida.
 
Her crew said the 62-year-old swimmer has completed at least 49 miles (79 kilometers) of the 103-mile (166-kilometer) passage of the treacherous Florida Straits. If all goes well, she hopes to complete her sea swimming odyssey Monday morning.
 
Updates have been coming from her handlers via Internet posts, and already Nyad has been in the water longer than her aborted attempt at a Florida Straits crossing last month, when she lasted 29 hours before a crippling asthma attack forced her to call it quits.
 
Nyad suffered a jellyfish sting that painfully affected her face and eyes that had to be treated late Saturday aboard a support vessel before she returned to the water overnight. Her team tweeted that she spent the pre-dawn hours slogging uneventfuly toward her goal of a Florida landfall, stroke by stroke. Her website said she had completed 37 hours in the water minutes after 7 a.m. Eastern Time (1100 GMT) Sunday - or roughly 100,000 strokes since leaving Cuba.
 
An independent observer said she could still pursue her attempted record-setting swim from Cuba to Florida despite seeking treatment.
 
Nyad's team said early Sunday in a website update that a so-called "staged swim record" would still be valid as long as she was on the boat only for treatment and not to rest - rather than a nonstop record. It didn't elaborate on the specific treatment she received or how long she was out of the water, but added she resumed her swimming quest at the exact spot where she had paused for medical help.
 
"The rules say she is now going for a record staged swim rather than a non-stop swim," the updated noted.
 
Her organizers said making it through the second night was a big hurdle as she struggles with the physical and mental challenges of the distance involved. Her web site said she spent the night trying to recall favorite songs and thinking upbeat thoughts while slipping through the waters under a nighttime sky bristling with stars and a sliver of a crescent moon.
 
Just ahead of dawn, the team reported online that she was still at it with little new to report.
 
"For now, no news is good news," her team reported online. "At this moment, Diana might be playing Neil Young in her mind or contemplating Stephen Hawking's theories of the cosmos."
 
Nyad is making her second attempt in as many months at the Cuba-Florida crossing, a lifelong dream that she first tried as a 28-year-old back in 1978, when she swam inside a steel shark cage for about 42 hours before ending the attempt. A cageless attempt this past August fell short 29 hours in when, gasping for breath, Nyad threw in the towel after an 11-hour asthma attack she blamed on a bad reaction to a new medicine.
 
Earlier in her trip, Nyad had a run-in with a Portuguese Man o' War that she called "scary" and which left her with stings on her face, arms and side. Complaining of difficulty breathing, she received oxygen and a steroid shot from her doctors and tread water while she recovered from that earlier Man o' War sting.
 
On Saturday, handlers spotted barracudas in the area and she got a visit from a curious Oceanic white tipped shark that was shooed off by a support diver. Three so-called "shark divers" were reported to be protecting her in the water early Sunday.
 
Without a cage to protect her, Nyad is relying on equipment surrounding her with an electrical field that is harmless but deters most sharks. Her divers are there to gently discourage any who make it through. But not all encounters with marine life were unpleasant. Earlier in her journey, 10 pilot whales emerged in the distance ahead of the swimmer, according to one team tweet.
 
The Los Angeles woman normally pauses every 45 and 90 minutes to rest and refuel on food that her assistants pass to her in the water, but without getting on the boat. For strength she is regularly being fed with pasta, bananas, bite-size pieces of peanut butter sandwiches and high calorie and high carbohydrate liquid refreshments.
 
Meanwhile, kayakers were reported to be counting every stroke as she swam continuously overnight. And her support team was getting more foodstuffs ready for the second half of her quest.