The gemara says that generally if a person builds a succah type structure which infringes on his friends property, their is a grace period of 30 days in which the owner graciously permits the machzik to use the area and doesn't have to protest. But, after that grace period has passed, if the owner doesn't protest, the machzik will have a chazaka to be able to claim that he purchased the rights of use. But, if the succah is built for succos, then immediately after the 7 days of succos passes, the lack of the owners protest enables the builder to claim that he purchased the right to leave it there permanently (this is according to rashi, but the hagahos ashri cites other opinions that it is 7 days in addition to the 30 days).
Tosafos points out that in truth the builder doesn't have a chazaka after 7 days, he only has a chazaka after 8 days since on the 8th day which is shemini atzeres it wasn't possible to remove the succah. The Ya'avetz asks what compels Tosafos to say that he will not have a chazaka until the eighth day is over. Perhaps we assume that the owner would have allowed him to use the space for the mitzvah, but as soon as the mitzvah ends the owner is expected to protest. The fact that the owner fails to protest would not enable the builder to claim that he has acquired permanent rights to this area?
It would seem that Tosafos holds that although the owner can make a macha'ah to protest the succah immediately after the 7 days pass, even before the 8th day ends, he is not expected to do so. Why? Because he is well aware that his protest is futile. The owner can claim that for the duration of succos he allowed the machzik to fulfill his mitzvah; on day 8 he also did not protest because he knew that his protest would be in vain since the machzik could not remove the succah until after succos. Therefore, Tosafos holds that the owner has the right to protest through day 8. From this we can learn that even after one has been machzik for enough time to create a chazaka, it is only effective if by the owner protesting he could have forced the machzik to leave. But in a situation where the owner could not have forced the machzik to leave, such as when the chazaka concludes on a shabbos or yom tov, the owner is not expected to protest and is given an extra day to voice his protest.