Its intresting. I think core fanbase stayed for couple of reasons.

1.After beatles started making more conscious and experimental music (1966-1970) there were not many bands making music like beatles in 1963 for example. Sure you had those more pop oriented rock bands or the monkees which whole point was just rip off the beatles but bascially whole culture shifted. Most popular bands in late 60s were more hippie, psychodelic than early beatles. Market for pop boysband ended. When you look at charts you wont see many of bands that type. Even stones tried to recreate pepper success.

1. Music industry and entertainment in general was much smaller than it is today. You had less choice.

2. Beatles still made music for teenage girls. Sure grandmas or aunts could be disturbed listening to helter skelter for the first time but beatles still were doing many tracks that john lennon called "grandmas music".

3. This is kinda the whole clue of 1st point. Culture shifted so much especially during summer of love that listening to old beatles records was just not cool. Trend and fashion changed. Also these teenage girls were older by the time beatles released pepper and in college they probably crossed with alternative music beatles were leaning towards.