(Related question: Who invented Star Trek sideburns and why?)
The pointy sideburns didn't apparently exist in ENT:
But did exist thereafter:
Hairstyles don't normally persist for ten years, let alone one hundred. Is there any in universe explanation for why this style is so popular for such a long period of time?
The OP is making a fairly reasonable observation about society-at-large:
Hairstyles don't normally persist for ten years, let alone one hundred.
Now, I'm going to go out on a limb and say that observations about society-at-large may not apply to the evolution of hairstyles within organizations such as Starfleet. Although Starfleet plays humanitarian and scientific roles in the Federation, it remains at the end of the day a military organization, and so it might be reasonable to assume that there are standard haircuts preferred by Starfleet officers. Certainly, an officer would at least be expected to keep his hair "neat". (We seem to be talking about humanoid male officers, and so I make that assumption throughout.) There are, as one might predict, regulations governing cadets' hairstyles. In the Voyager novel Pathways by Jeri Taylor, we find:
...Cadet Tom Paris turned to see his friend Charlie Day trotting toward him...Charlie jogged up to him, his round, cheerful face wreathed in a toothy smile, dusty brown hair managing as always to look shaggy and unruly in spite of the regulation haircut...
(By the way, unlike the authors of most Trek novelists, Jeri Taylor was actually a screenwriter for all three of TNG, DS9, and Voyager. She was the Co-Executive Producer, with Rick Berman and Michael Piller, and showrunner of TNG for its last season. She was also the Co-Executive Producer of Voyager for its first four seasons. Thus, she is a trusted source!)
While it is unlikely that there are exceedingly specific regulations regarding hairstyles of full-fledged officers, one might expect that the combination of (a) the discipline and rigour instilled by academy training, (b) the desire to maintain uniformity (i.e. to not stand out for the "wrong reasons"), and (c) a sense of tradition binding different generations of officers might lead to the development of certain preferred "officer's cuts":
For Starfleet, the standard "officer's cut" might traditionally involve shaped, pointed sideburns.
Of course, as one ages and rises through the ranks, one might decide to take certain liberties — or go bald, like Picard.
In any case, for information on the persistence of the pointed sideburn, one can always ask Mot directly:
They wanted something futuristic for the series, but at the same time these were real people who didn't wanna look like freaks from the future. the "Star Trek Sideburn" was a compromise. Beyond Star Trek, most of the major scifi series came about in the 1960's and 70's, at the time, sideburns and various hairstyles came into fruition and were acclimated to Science fiction long after the decade transpired. Women with Feathered hair and afro's became more common, bobed edges with loose spikes. For men, shoulder length and messy hair were more socially acceptable and by then, the rise in male attuned hair care products blossomed and men were accustomed to hairstyles that defied gravity which gave rise to helmet hair and sculpted mullets. Also the 70's was the end of an era for military and uniformed services permitting facial hair, sideburns, and various hairstyles.
