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.
One of the most successful boy bands of all time has survived a few losses. Robbie Williams walked away from the band before a tour and they continued without him. They enjoyed pretty much the same level of success as with him but then decided to go their separate ways after just a year. However, they then reformed (without Robbie) and went on to become a huge success again. Then Robbie came back, then he left again. Then Jason Orange decided to leave and the band is now carrying on as a 3 and to be fair they seem to be enjoying the same levels of success.