There are several reasons that have been brought up, which lead us to the believe that she’ll go down.
1) If she doesn’t go down, Zeff and all the people associated to the SHs will be in danger since Big Mom won’t forgive them ruining her tea party. We saw what she did to the one broker who missed her last tea party (and he even had a good reason): she sent him his dad’s head in a box. Now imagine her rage after Luffy & Co. completely wreck her party.
2) Kaido mentioning that “they only thing they’ve done is beating a shichibukai or two”. Kaido doesn’t take them seriously. Now, what would make him take them seriously? If Luffy & Co. manage to bring down an actual Yonkou, of course.
3) The time left in OP. If we take Oda’s comments seriously, that OP is already 70% done and look at the time left, it would be hard to fit in a second Big Mom arc.
Having said all of this, I still strongly believe that Big Mom won’t go down in this arc and there are strong arguments backing this claim up:
1) Do you remember the fights against all the other “big enemies”? Crocodile, Enel, Lucci, Doflamingo…they have one thing in common: It always took multiple tries and fights to bring them down and starting from the first encounter/skirmish it was still a very long time until they were defeated. It was nearly 40 chapters each time, to be exact.
Now we can safely assume that there aren’t more than 15-20 chapters left on WCI (since the editor said so) and Luffy hasn’t even met Big Mom face to face.
2) Big Mom is a Yonkou. One of the most important, most hyped and most powerful fighters in the entire OP universe. If you look at argument 1) above, you see that it took much longer to bring vastly inferior opponents down. There is no way that Oda dehypes one of his greatest and most hyped creations in letting her get defeated in less than 20 chapters. She isn’t even injured or weakened yet. A Yonkou isn’t going down in 15 chapters, when she hasn’t even fought yet.
3) We only have half of the crew on WCI. Again, Oda won’t let such an important event like the downfall of Big Mom happen, when half of the crew isn’t even there. It would be anticlimatic and it would massively dehype the Yonkou, including Kaido. Imagine Luffy & Co. arriving at Wano and telling the rest that they just brought down a Yonkou. This would kill almost all the suspense and make the downfall of a Yonkou seem random. Oda wants to show how dangerous they are and showing how strong Big Mom is also hypes Kaido even more.
Now, do I know how Oda will resolve the problems a pissed-off Big Mom will present? No, I don’t have an answer for this. I’m sure however, that Oda will come up with something very clever. There’s one thing I know, however: Big Mom won’t go down in this arc.
*Theory by dirtyLarry
I think they will be saved by the vivre card that Lola gave them on thriller bark, she said her mother is a famous pirate and that she will help them if they nees help