The snarker in me wants to say "about as long as it takes for a baby to become a teenager" ;D
But let's break it down a little further.
Let's make some assumptions (you might want to put some more deets in your question BTW, so I don't have to assume), just to make a game of it. Okay:
The designers of the utopia are legit nice guys, this is not some secret tyranny.
The physical needs of people and building are fairly well met. Nobody's starving, building is maintained, the community is adequately policed.
There's no "unfair underclass" of people who are put down because of religion, or color, or language, and so on.
Okay, what does that leave us to work with?
Envy -- Somebody has a better view. Somebody is closer to the hot-water pipes. Humans are pattern-seeing machines; we can construct a pattern, or conspiracy theory, from three data points. Might be some latitude for unrest there. Any inequality -- any inequality -- in lifestyle, education opportunities can be exploited.
Jealousy -- Folks want to keep what's theirs. Specifically, you want your kids to have every advantage over the next guy's kids. Guess whose kids will be best situated with opportunity? Yep, the administrators'. Cue envy, above. ;D
Social Control -- this is endemic to utopian societies. The founders have a vision, right? They want that vision to endure, right? Well, you have to keep the hoi-polloi in line with the vision. Whether it be with propaganda, taxation, instant executions, or whatever ... The Plan will have some provision to coerce people to follow along with how the Founders believe people should behave. People are smart (pattern-seers, roit?) and will notice that they're being influenced. Some of them will resent it.
Changing Conditions -- This is the killer. Utopias are usually designed by angry, bitter philosophers who are furious about the state of the society the came from. So their utopias will be engineered -- dare I say overengineered? -- to combat what they hate most about their current society. Their vision will become less and less relevant to the changing conditions of the building as the years go by. But, per above, is still being enforced. Uh-oh... Ex: Let's say the building was made as an "environmental redoubt" to shelter the remains of the human race and lower its footprint on the world. So extreme recycling and resource rationing is enforced. Over time, as people realize that the world has healed, and is empty, beckoning for recolonization, but the leaders still won't let them out...
Out-of-context problem -- Related to changing conditions. What if there's a huge earthquake, which opens huge gaps in the walls? What if solar activity lessens, so the solar panels can't get enough juice? What if the residents can see towns spring up outside the building which look really fun? All these things stress the society.
So ... what does all this add up to?
Honestly, I give it 3 generations, tops. First (founding) generation is full of zeal for the plan. Second generation is used to it; they're not excited about the utopia. It's just boring humdrum life to them. The big problems are all solved, ambitious people are starting to squabble over smaller and smaller stakes. Third generation is restless...
I encourage you to check out "The Fourth Turning", which posits a generational clock in American society!