One band worth considering could well be:
All the six founding members stayed in the band together for 20 years — 1977 to 1997 until lead singer Michael Hutchence's death. They were still active for 15 years after that, but haven't been on the scenes again since 2012. In addition to the lead singer's replacement(s), this wiki reference does include the names of some additional touring members too, but that really shouldn't take away anything from the initial core group.
I was initially also thinking that U2 have been intact since their inception. This may or may not be technically true, but can make up for a very strong and interesting argument. The summary is as follows:
- Six guys from a high school got together to form a band called Feedback in 1976.
- Wiki is more or less quiet about Ivan McCormick, whose name features in the past members, but doesn't indicate when or how he left the band (in the first year itself). However, a further search brings up this press article narrating the sorry tale of a young teenager who, for being too young, couldn't be a part of the group when they were to perform in a pub.
- At some point in 1977 (not sure before or after Ivan's omission), Feedback rebranded themselves as The Hype.
- Dik Evans, elder brother of David Evans — one of the "face" of the bands now, being a few years older than the rest of the "then young" guys was gradually phased out on good terms from The Hype. To quote wiki:
In April 1977, Feedback played their first gig for a paying audience at St. Fintan's High School. Shortly after, the band changed their name to The Hype. Dik Evans, who was older and by this time at college, was becoming the odd man out. The rest of the band was leaning towards the idea of a four-piece ensemble. In March 1978, the group changed their name to "U2".
Dik Evans was officially phased out of the band with a farewell concert at the Presbyterian Church Hall in Howth. During the show, which featured The Hype playing cover songs, Dik ceremonially walked offstage. The remaining four band members returned later in the concert to play original material as U2.
The above quotes from Wiki can make up for a case that, perhaps U2 had always been thought of as a four member group — comprising of Bono, The Edge, Larry Mullen Jr. and Adam Clayton. Cherry on the cake: all of these four members, even though they first united in 1976, have still been in the band together ever since the formation of U2 in 1978!
Now, this accounts for.... not legitimately 41.... but still a jaw dropping 39 years of U2!
PS: Thanks to the question, got a chance to look at my old collection and revisit some memorable songs ;)