I have six children and just recently several of them had low grade fevers long term ( 100.3 f ) off and on ..... at different time periods . It turns out that all the four children who were sick even though only some of them had contracted strep .... had a urinary tract infection that they themselves could not recognize or feel and all of the four children who were sick had off and on chest cold problems. Sort of a secondary bacterial infection in reaction to lowered immune system by winter viruses.
I also have a 3 year old with severe every single day cough not all day but ... she has been tested for reflux, cystic fibrosis , everything. because of the pnuemonia she had as a child her heart became slightly enlarged as well. She still to this day is growing slowly out of it, a happy active girl you'd never know is sick. and things like expectorants and nasal decogestants really to help the asthma meds when used correclty or even on their own can prevent the need for asthma meds as often.. a daily inhaled steroid is what finally fixed everything.........................................................
I noticed that when I controlled everything like laying a blanket on the couch in case of dust , as well as things that make you reinfect yourself with the same cold for months like doorhandles you might not notice on a certain side of the car or the phone at work are always used will make a grown adult reinfect themselves over and over imagine what a child might be using daily to reinfect themselves it will prevent improvement of any virus
I am having the same problem with my just turned four year old. She has asthma and gastroesophogeal reflux. I just want to mention that anytime a child has asthma or a long term cough they should be checked for reflux. Since she has been on prevacid she doesn't cough as much. My daughter had a sinus infection but for the last month still has this on again off again fever. Same thing as you see. I am not sure the answer, but my doctor today is having a blood test to check blood cell counts and also I requested him to do a urinalysis to check for a bladder infection. I will let you know how it pans out next week. Sounds like the same thing I am going through.
I live in the UK, normally when children present with an ongoing cough, especially at night the diagnosis is usually asthma and medicine or inhalers are given but I expect they must have discounted that as an option possibly because of the associated fever but it might be worth mentioning or exploring. It's just an idea.
you may want to have her checked for a sinus infection......if she has a cough off and on it could be from post nasal drip......her sinuses may be the cause...especially the night time cough.........good luck