In my experience, only really strong fragrances that I don't like will live on to offend my new soap. I have had that happen to me once; I soaped a fragrance that I found cloying and gave me headaches and stuck really strong in the soap. After cutting the soap I let it sit for 6 months and the odor remained super strong and still gave me headaches if I was around it too much. So I hoped that in the reheating process of rebatching, it would weaken enough to not offend. Well it did weaken some, but it is still very strong and I still don't like it.
But with fragrances I have liked, none have ruined a new batch of soap. Some fragrances last well and some don't, so if you know which kind your is, then proceed accordingly. What I have done and read that others have also done, is to add either more of the same fragrance or a complementary fragrance to the new soap.
One thing I have learned is to keep my soap shavings in containers in similarity groups. For me it's color, but one could also do it by fragrance similarities as well. Then when I want to make a soap with blue bits, I have the blues altogether. Another thing I've come to realize is that saving all the shavings may be an excessive endeavor not worth the trouble. So sometimes I just decide to toss them and not save all of them.