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.
If you thought the Take That members situation was bad then you might not want to know about the Red Hot Chili Peppers. In the history of this band there has been 7 different guitarists and 5 different drummers. The only two remaining band members are Anthony Kiedis and Flea. They are still going strong though despite losing numerous people along the way.
