I think that, in general, MOO has it right on the nose. Few bands get the luxury of a slow dive. Most just get tossed to the wastebin before they have a chance to get better.
That said, let us look at some GOOD bands (obviously - highly subjective). The exceptions who have had a long career
Beatles - Probably got Better with years
Rolling Stones - Got better and then a long, long decline. They are still pretty good, but not as amazing as they were at their height.
U2 - Chamelon-like. Started as protesters, moved to rock gods, shifted to electronica and pop, and then back to rock. Probably a long decline, like the Stones.
Radiohead - Climbed to the very top and now in a steep decline
REM - Really, a long climb to greatness and then a pretty steep deline to mediocrity
I would say that most GOOD (once again, subjective) bands tend to decline gradually.
I would attribute this to losing connection with the youth as they age. Popular music must resonate with the young if it is to be relevant.
Also, as bands age, their success leads them to a wealthy lifestyle, they stop having the same problems as teens, and they have to work a lot harder to write relevant stuff. They have a built in audience that will buy their stuff pretty much no matter what, so the effort to stay current has less pull.
That is my opinion, anyway.