Despite the longevity of Vulcans, they seem to progress through Starfleet ranks at a similar rate to that of humans. With a later onset of senescence, one could expect Vulcan officers to remain on active duty much longer than their human counterparts.
Given all this, why isn't the Admiralty of Starfleet composed almost entirely of Vulcans?
The questions posted in the comments help to answer this question:
Additionally, two of the three major Vulcan characters in Starfleet (T'Pol and Spock) were both strongly discouraged from joining (T'Pol largely due to strong prejudices against humanity during the pre-Federation era). Because Starfleet started as an Earth organization and with longstanding Vulcan prejudices against humans (apparently we smell bad and are uncivilised) and Starfleet itself, Vulcans simply weren't enlisting in the same numbers as humans were. Science and diplomacy are apparently more respectable professions for a Vulcan. So even if they did enter Starfleet, they'd probably gravitate towards those specialties rather than command. Even Tuvok started off as a science officer.
Plus, TNG and DS9 implied that Vulcans and other species commanded their own fleet of Starfleet ships. It's possible that there are regional divisions in the command structure.
Out of universe, a lot of the named Admirals in the series are simply named after producers and others who worked on the show (e.g. Peter Lauritson, Rick Berman, Michael Piller, Richard James, Marvin Rush, etc.), all of whom happen to be human.
Simply put: Vulcans did not have interest in space. For a society where greatest challenge, honour and reward are self-improvement and seeking perfection, service on a spacefaring vessel would be hindrance rather than help in attaining those goals. Any shipboard duty leaves rather small amount of free time; just ask anybody with experience in navy.
And as always, there are exceptions. Obviously.
And no, Starfleet did not encourage homogeneous crews (DS9 case of all-Vulcan ship was special dispensation IIRC), as is implied in other answer. I don't know if ENT finally made canon, but even with that discarded, it's clear that Federation came to be as a solution to one-race-crew-ships problems in the first place.
Somewhat different was diplomatic/political service — those offered better opportunities to perfect oneself (patience and smell, especially), and were much less time-intensive. So they could be viewed more favourably.
EDIT: Eating a frog here. It seems that canon indeed allows, even insists on segregated crews (from Gene Roddenberry himself: https://i.sstatic.net/yHln0.jpg). Shows how much problems creates sticking to the rules invented so long ago that no one remembers them.
