>If you choose not to accept it again then the falsification doesn't occur.

Yes, which is the same problem that induction and verification has. You can infer and verify something then later find out that you can no longer accept it. It applies just as much to falsification as verification.

>One experiment! If you do another experiment it's not a re-litigation of the previous falsification at time 1, it's actually just another falsification at time 2

Well if you are talking about the same type of phenomenon explored several times, I don't see how it is different from the classic example in induction about the sun not rising the next day. In the induction example, sun rises on day 1 but not day 2, in the falsification example instance 1 might be the orbit of some planet and instance 2 might be the discovery that the orbit is affected by some other body. in neither example do verification or falsification are capable of permanently cementing the status of the theories. the finding of the sun not rising on day 2 might even be reversed if it rises on all the days after that and you find some good explanation of why it did not rise on that particular day. my example with the planet orbits depicts a single incidence of newtownan mechanics being falsified which can conceivably be reversed, or was actually reversed depending on how correct my example was.