My daughter has similar situation. She is 2.5 years old now and started nursery in Sept. Initially she got fever every Sat/Sun. We give them the medicine (only for fever) one or two times and she will recover. However, since last time (now is the second time), she needs to see the doctor to get the antibiotics (as quite serious, e.g 39 degree) and the medicine does not work. She also does not have other symtom (e.g. running nose).
I guess maybe she gets the virus from the other classmates.