The reason bands become successful will usually be a combination of their talent and their likability. Losing a member can be a huge blow to a band whose fame (and usually fortune) are based on the group as a whole. Many groups have simply split up or suffered failing careers after losing a member but other have gone on to have the same, if not more success. Take a look at these bands who have successfully survived the loss of a band member.
When Oasis released their debut album Definitely Maybe in 1994 they had Tony McCarroll as a member. He played drums on the first album but had left by the release of the second and replaced by Alan White, as allegedly there was tension between him and Noel Gallagher. The loss of this band member didn’t affect Oasis in any way and the band went on to achieve very high levels of success.