We had the same problems and so took our children out of childcare (it ended up cheaper to hire someone at home in any case, paradoxically). After that we had nearly zero illnesses in a whole year. The viruses have a latent phase so they spread before the child has symptoms, and some survive just long enough on surfaces like trolley handles and the rails of escalators to spread. But it's usually toys, and parents who lie about their kid's health due to work pressures.
Also, not all vaccines give life long immunity (in some people they don't even work), but having had some exposure to the antigen, the body is faster in responding to the real virus and so you only get mildly sick. And how a child reacts to anything is a bit unpredictable because the immune system of each person is differently honed - some people react violently to a virus whereas others have hardly a sniffle. That's part of the "herd survival" build into our genes.
It's worth remembering that the two biggest things that have improved the health and survival of people in the modern world were sanitation and nutrition. Vaccines are often credited with the success too, but I'm not so sure they are that important. Because we don't see any of those viruses anymore (when did you last see 1% of your city's childhood population die of Measles?) it's easy to consider vaccines as risky and bad. It's a gamble that people in the past were more than willing to take, just not so much today.
I have read the various articles that are around like "The Vaccine Hoax
", and I sort of half believe them. What worries me is that something like a mass vaccination program is a huge vulnerability in a society. What if someone got in and did something to those vaccines... when would we find out about it?