Shafei, Hanbali, and Maliki, schools: You don't have to replace, but are mustahab to do.
Hanafi: Youh have to replace.
Special case: If it was a Nuthr (vow نذر), then all the four schools agree that you have to replace.
Both opinions have evidences from Hadiths, but I will not translate them now, you can see them in the book below.
The majority say you don't have to, but are recommended to do. This majority say that the Hadith which tells that you have to replace (on which those who said you have to depend), doesn't mean "have to", but rather "mustahab to".
Al Mogni by Ibn Qudamah | Vol.3 | P.44 (A compared Fiqh book, in which all schools' opinions are mentioned an compared).