OK, so there really isn't one.
It seems as though Maddie's latest mystery fever -- which spiked at 105 last Saturday night and didn't go down with Tylenol -- was random. A few of the other neighborhood kids had fevers with no symptoms, too, and Matt ended up getting it (go figure; he's always sick). The doctor believes that her three high fevers in a month's time were just coincidence.
In order to come to that conclusion, Maddie had her blood drawn once and gave two urine samples. After the first urinalysis, the doctor noticed some things that could suggest diabetes, so she recommended the blood draw. Maddie was a trooper, and though she cried, she didn't fight it. "My" (what she calls Grandma Schaefer) was along, and she sat on her lap during the draw. Macy, my sympathetic crier, shed a few tears as well.
So we learned that Maddie is anemic. We bought her a new daily multivitamin with iron, so hopefully that helps. She's kind of disappointed she can't eat her gummy vitamins anymore; I could only find Flintstones vitamins with iron. But she knows the doctor said we have to take a new vitamin, and she seemed to like the Flintstones well enough despite the texture change. She'll have to have her blood drawn again in a few months to see if her iron levels are within the normal range.
Thanks to everyone for the thoughts and well wishes when Maddie wasn't feeling well and I was a bit nervous about it. :)