There seem to be two main ways that questions about “long term effects of vaccines” can be intended or interpreted:
1) Has it been conclusively shown that all vaccines are absolutely harmless and will never cause or contribute to significant health problems at any point in any vaccinated person’s life?
2) Are any medical studies being done on possible statistically significant connections between vaccines and particular health problems over the long term, meaning several years or decades after the vaccination?
The answer to (1) is “No” and will always continue to be “No”, because you simply can’t prove that any medical treatment is 100% safe for everybody forever. However, many antivaxers seem to think that the lack of a “Yes” answer to (1) is sufficient justification for distrusting vaccines, or at least provides the excuse they’re looking for to regard vaccines with suspicion.
The answer to (2) is “Yes” and will always continue to be “Yes”, since of course medical researchers who study such health problems want to know all about their causes and contributing factors. Many examples of such studies have already been provided in this thread, as everybody but curlcoat is well aware.
Now, AFAICT there is no systematic comprehensive program of studies designed to explore all possible lifelong health impacts of vaccines within a given timeframe, because such long-term studies aren’t required in order for vaccines to be approved.
Which makes sense: antigens are most likely to produce side-effects in the short term, after all. It would be silly to delay acceptance of a vaccine that has been shown to be effective in preventing a dangerous illness, and to have no serious side-effects in the short term, just because we’re not yet absolutely sure that it can’t possibly have any longer-term negative effects.
Again, as Kolga and LavenderBlue point out, such a systematic comprehensive program of studies of all possible vaccine side-effects seems to be what antivaxers are demanding. When they say “there are no long-term studies” of vaccine effects, this is what they mean.
And the more that curlcoat goes on repeating the same previously answered question about long-term studies, the clearer it becomes that she’s ignoring the “Yes” answer to question (2). What she’s trying to do instead is demand a “Yes” answer to question (1), and pretend that its impossibility somehow counts as a “gotcha” against vaccine proponents.