I was also going to suggest ear ache or teething and also allergies??? I know that both my kids and myself will get cold like symptoms when our allergies attack...like this past week with the Santa Ana winds blowing in :(. My 2 yo daughter will also get pretty high fevers in the 102 range from this. We got both my kids food and environmental allergy tested in the last 6 months. They can do the blood test at 1 years old, but can only do the back scratch test after 2 years old. My 4 yo son showed no allergy reactions in his blood test, so no back scratch needed. My 2 yo daughter showed allergy reaction to nuts, wheat, egg and soy in her blood work. So we did the back scratch test for all the major food allergens, the common types of nuts, common environmental stuff, and common food dyes and preservatives. She had a reaction only to cashews. Then we did 2 months of food elimination/reintroduction of eggs, soy, and wheat. Two of elimination of all 3. Then I started off with eggs for a week. No reaction. Then soy for a week, no reaction. Then wheat. Immediate reaction. Her severe diaper rash and diarrhea came back within 24 hours and her ezcema broke out in her usual spots.
Basically allergies cause your body to think that it is sick and so the brain sends out signals to the body to overcompensate....fever, tiredness, rash, etc. to help flush out the toxins. So find that when our allergies are under attack for prolonged periods of time that's when we get sick.
I also have food allergies, and when I have been "bad" with my diet and have eaten stuff I am allergic to, I will get moderate to severe cold like symptoms. Chocolate does this to me. And I am intolerant to wheat/gluten so although it would take me eating a lot of wheat to make me sick, it can happen. If I eat more than 2 pieces of chocolate (like 2 Hershey Kisses), I will come down with cold like symptoms.
Anyhow, so maybe she's allergic to something either in her diet or in her immediate environment and every few weeks her body has had enough of it and reacts.
I hope you find the reason soon. I can't imagine how frustrated and worried you are.