I felt like most bands that stick around that long do so because of the first 3 albums, one or multiple of those early albums are popular enough and fuel their career to stick around over time, touring some and putting new albums that are decent but never as good as the earlier one that got them popular.

The ones coming to mind for me are all the like 2000-2013 emo/pop-punk/post-hardcore bands that are still making music... taking back sunday, my chemical romance, underoath, the used, etc...

oh also weezer probably... lots of rock bands seem to fit that in my mind - not as many as I originally thought though as I looked through