It's still daycare. Even if it's all of the above, kids get sick in daycare, or sunday school, or the McDonald's playland.
Kids get sick, because other parents send their child to daycare (sunday school mcdonald's) with a cough, or fever, or anything else they decide isn't important enough to keep them home for.
Parents tell me all the time "She's just teething". One parent told me "it's her four year molars" (she's 18 months old)
Kids catch things from other kids. But, the advantage to catching it while they are little is usually their immunities are built up by school age and they don't get sick as often as a kid who has never been sick.
My best friend's child was vaccinated. He was never breast fed. He was in my daycare from four weeks on, he ate a HORRIBLE diet. He literally ate hotdogs every night for four years. Yet, he was never sick. He never missed school because of illness. (i'm very jealous of him

)
My own kid, was and still is the sickest child I have ever seen. She has had even bizarre illnesses that make the doctors go and bring in other doctors. She's had West Nile virus, and menengitis, and had her tonsils out at 9 months old.. she is just a very sickly kid.
The only thing I can think of is the MMR. She was fine until the MMR. I don't fully understand it yet. But, that is the only thing I can remember that stands out in my mind as being a turning point.
I want to know what happened, I really do, but nobody seems to know why she's so sick all the time. I wish I could go back and re-do everything.