If a female dog gets pregnant, can the traits of the first litter carry onto the second?

I have a female pitt bull that is more like my kid than anything. I recently moved into a house that had another (male) dog. The dog is a mutt and ended up getting my dog pregnant. I only wanted to breed her one time, preferably with another pitt bull. Somebody told me that I can no longer breed her if i want a full blooded pitt bull because the genes from the male will last for six litters. Is this true?