I have to correct you: it is now common for adults to catch illnesses they've been vaccinated against as a child. This may be partly because the viruses mutate over time. I myself have had measles and whooping cough as an adult despite being vaccinated as a child. I was told by my doctor that both diseases are now common in adults who were vaccinated as children. It is well known that most vaccinations only give protection for several years and that viruses can mutate over time to 'escape' the vaccine protection effect.
If I understand this correctly, there's a few things going on.
Some diseases need regular boosters eg pertussis, tetanus.
Some vaccinations are not 100% effective eg measles works for 9/10 people per shot, so with a 2-shot schedule it has a 99% effectiveness rate.
Some diseases mutate over time hence we need to keep improving vaccines.
The answer really is to vaccinate as many people as possible to achieve herd immunity.
Measles is NOT common in the US even though the vaccine has the same failure rate here as in the UK - because we have effective herd immunity.
Pertussis has been increasing here, so they have been encouraging the Td booster even before people hit their 10 years.
Chickenpox is very uncommon even though the vaccine doesn't provide 100% immunity, because herd immunity is effective (helped by schools having aggressive exclusion policies for infected students).
All of which are arguments for people getting vaccinations, and staying up to date with their boosters - not only to prevent themselves from getting the disease, but to prevent others who for whatever reason cannot achieve immunity.