So she is your new ducklings? how old are the others? have you tried using some warm salt water to wash her eyes using a soft cotton ball. also some eye salve or neomycin with out pain relief may help. I'd get some poultry vitamins or save a chick and start adding them to her/all their water and make sure is isn't too warm or too cool. do you have a thermometer in your brooder. Could one of your other ducklings pecked this one in the eye.
temp should be around high 70's low 80's if too hot that can make them sluggish and if way too hot can kill them, but your other ducklings are acting normal right? so temp maybe fine. as far as if she can die, I cannot say, I hope not but it does sound like she isn't feeling so good. Has she always been like this since you got her? can you put her into a nice warm tub of water where she can wash her face real good. But only if you feel she is well enough. Never leave a duckling unattended even for a second in water .
Aww I hope you find her feeling better. are you sure the other ducklings aren't picking on her or keeping her from food and water? I'd watch for a while when you get home just to be sure.
go to feed store and get Terrimycin eye ointmert and start using it.
