Interesting question. I saw The Jets in concert a few years back and the guitar player was the only member on stage who was around during their "Crush on You" heyday. I did a quick search and found that there are quite a few bands with no original members, including The Hollies, Iron Butterfly, Gwar and Quiet Riot.

My thought is that a band is basically a corporation, putting out a product and using specific branding. In other businesses in different industries people leave, new people are hired, leadership strategies change and companies re-structure to stay viable. So why not a band? Also, consider Saturday Night Live: it evolved over the years, but is still basically the same show long after Dan Aykroyd and the rest of the original cast left.

I see your point: Music is something very personal and is deeply tied to its creator. But I think if there's a direct lineage to the original creators (and they're making an effort to add to the band's catalog), it can still be considered the same band.

This is a good point. Queen is down two members and they perform nowadays as "Queen + Adam Lambert" - acknowledging that it's not the same as before and that a new guy is filling in a role.